Test Bank For Precalculus, 11th Edition

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the function with the graph that best describes the situation. 1) The amount of rainfall as a function of time, if the rain fell more and more softly. A) B) C) D) Answer: B Explanation: A) B) C) D) 1 1) The graph of a function f is given. Use the graph to answer the question. 2) For which of the following values of x does f(x) = 10? 2) 25 25 -25 -25 A) 10 Answer: C Explanation: B) 35 C) 20 D) 25 A) B) C) D) Match the graph to the function listed whose graph most resembles the one given. 3) 3) A) square function C) cube function Answer: A Explanation: B) reciprocal function D) absolute value function A) B) C) D) 2 Match the correct function to the graph. 4) 4) A) y = x Answer: D Explanation: B) y = x + 1 C) y = x – 1 A) B) C) D) Solve the problem. 5) Let P = (x, y) be a point on the graph of y = a function of x. A) d(x) = x2 – x + 1 x. Express the distance d from P to the point (1, 0) as B) d(x) = x2 – x + 1 D) d(x) = x2 + 2x + 2 C) d(x) = x2 + 2x + 2 Answer: A Explanation: D) y = x – 1 A) B) C) D) 3 5) Match the graph to the function listed whose graph most resembles the one given. 6) 6) A) absolute value function C) square root function Answer: D Explanation: B) square function D) reciprocal function A) B) C) D) 7) 7) A) constant function C) reciprocal function Answer: D Explanation: B) absolute value function D) linear function A) B) C) D) 4 8) 8) A) cube root function C) cube function Answer: D Explanation: B) square function D) square root function A) B) C) D) 9) 9) A) square function C) reciprocal function Answer: D Explanation: B) linear function D) absolute value function A) B) C) D) 10) 10) A) cube root function C) square root function Answer: D Explanation: B) square function D) cube function A) B) C) D) 5 Match the correct function to the graph. 11) 11) A) y = |2 – x| Answer: A Explanation: B) y = |1 – x| C) y = |x + 2| A) B) C) D) 6 D) y = x – 2 Match the function with the graph that best describes the situation. 12) The height of an animal as a function of time. A) B) C) D) Answer: C Explanation: 12) A) B) C) D) Match the graph to the function listed whose graph most resembles the one given. 13) 13) A) linear function C) constant function Answer: C Explanation: B) absolute value function D) reciprocal function A) B) C) D) 7 14) 14) A) cube root function C) square function Answer: A Explanation: B) cube function D) square root function A) B) C) D) Match the correct function to the graph. 15) 15) A) y = -2×2 + 1 Answer: A Explanation: B) y = -2×2 – 1 C) y = -2×2 D) y = 1 – x2 A) B) C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 16) Two boats leave a dock at the same time. One boat is headed directly east at a constant speed of 35 knots (nautical miles per hour), and the other is headed directly south at a constant speed of 22 knots. Express the distance d between the boats as a function of the time t. Answer: d(t) = 1709t Explanation: 8 16) 17) A right triangle has one vertex on the graph of y = x2 at (x, y), another at the origin, and 17) the third on the (positive) y-axis at (0, y). Express the area A of the triangle as a function of x. Answer: A(x) = 1 x3 2 Explanation: Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. 18) f(x) = x5 – x2; (-2, 2) 18) Answer: local maximum at (0, 0) local minimum at (0.74, -0.33) increasing on (-2, 0) and (0.74, 2) decreasing on (0, 0.74) Explanation: Solve the problem. 19) A cellular phone plan had the following schedule of charges: Basic service, including 100 minutes of calls 2nd 100 minutes of calls Additional minutes of calls 19) $20.00 per month $0.075 per minute $0.10 per minute What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls. Answer: $27.50 $32.50; 20 C(x) = 12.5 + 0.075x 7.5 + 0.1x if 0 x 100 if 100 200 Explanation: Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. 20) f(x) = x3 – 4×2 + 6; (-1, 4) 20) Answer: local maximum at (0, 6) local minimum at (2.67, -3.48) increasing on (-1, 0) and (2.67, 4) decreasing on (0, 2.67) Explanation: 9 Solve the problem. 21) The price p and x, the quantity of a certain product sold, obey the demand equation 1 p=x + 100, {x|0 x 1000} 10 a) b) c) d) e) 21) Express the revenue R as a function of x. What is the revenue if 450 units are sold? Graph the revenue function using a graphing utility. What quantity x maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue? Answer: a. R(x) = – 1 x2 + 100x 10 b. c. R(450) = $24,750.00 d. e. 500; $25,000.00 $50.00 Explanation: 22) A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and 22) the other piece will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle. What is the domain of A? Answer: A(x) = 4 3 + 9 x2 – 15 x + 25; {x|0 x 20 } 16 2 3 Explanation: 23) The wind chill factor represents the equivalent air temperature at a standard wind speed that23) would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is if 0 v < 1.79 t W(t) = 33 – (10.45 + 10 v – v)(33 – t ) 22.04 33 – 1.5958(33 – t) if 1.79 v 300 Explanation: 30) A gas company has the following rate schedule for natural gas usage in single-family 30) residences: Monthly service charge $8.80 Per therm service charge 1st 25 therms Over 25 therms $0.6686/therm $0.85870/therm What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas. Answer: $25.52 $42.69 C(x) = 8.8 + 0.6686x 4.0475 + 0.8587x if 0 x 25 if x > 25 Explanation: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Complete the square and then use the shifting technique to graph the function. 13 31) f(x) = x2 – 10x 31) A) B) C) D) Answer: C Explanation: A) B) C) D) 14 The graph of a function f is given. Use the graph to answer the question. 32) What is the y-intercept? 32) 5 5 -5 -5 B) 3.5 A) -4 Answer: C Explanation: C) -3 D) 5 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 33) f(x) = 1 + 1 33) x+3 15 A) B) C) D) Answer: D Explanation: A) B) C) D) 16 The graph of a function f is given. Use the graph to answer the question. 34) Find the numbers, if any, at which f has a local maximum. What are the local maxima? A) f has a local maximum at x = -3 and 3; the local maximum is 0 B) f has a local maximum at x = 3; the local maximum is 1 C) f has a local maximum at x = 0; the local maximum is 1 D) f has no local maximum Answer: C Explanation: A) B) C) D) 17 34) Use the graph to find the intervals on which it is increasing, decreasing, or constant. 35) 35) A) Decreasing on (- , 0); increasing on (0, ) B) Increasing on (- , 0); decreasing on (0, ) C) Decreasing on (- , ) D) Increasing on (- , ) Answer: D Explanation: A) B) C) D) Find the average rate of change for the function between the given values. 36) f(x) = 1×3 + 2×2 + 4; from -7 to 6 A) 146 3 Answer: C Explanation: B) 533 6 C) 41 36) D) 292 13 A) B) C) D) Determine whether the equation defines y as a function of x. 37) y = 5x – 4 x+1 A) function Answer: A Explanation: 37) B) not a function A) B) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 18 38) f(x) = -(x + 3)2 – 1 38) A) B) C) D) Answer: D Explanation: A) B) C) D) 19 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 39) 39) A) function B) function domain: {x|x 9} range: all real numbers intercepts: (-2, 0), (0, 8), (4, 0) symmetry: y-axis C) function domain: all real numbers range: {y|y 9} intercepts: (0, -2), (8, 0), (0, 4) symmetry: none Answer: B Explanation: domain: all real numbers range: {y|y 9} intercepts: (-2, 0), (0, 8), (4, 0) symmetry: none D) not a function A) B) C) D) Find the value for the function. 40) Find f(-x) when f(x) = -3×2 – 2x – 2. A) -3×2 + 2x + 2 B) 3×2 + 2x + 2 Answer: C Explanation: 40) C) -3×2 + 2x – 2 A) B) C) D) 20 D) 3×2 + 2x – 2 Solve the problem. 41) Elissa wants to set up a rectangular dog run in her backyard. She has 22 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x. A) A(x) = 12x – x2 B) A(x) = 13×2 – x C) A(x) = 11x – x2 Answer: C Explanation: 41) D) A(x) = 10x – x2 A) B) C) D) The graph of a function is given. Decide whether it is even, odd, or neither. 42) 42) A) even Answer: C Explanation: B) odd C) neither A) B) C) Solve the problem. 43) If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 70 – 4.9×2 . What is the height of the rock when x = 1.5 seconds? Round to the nearest hundredth, if necessary. A) 62.65 m B) 59.2 m C) 81.03 m D) 58.98 m Answer: D Explanation: A) B) C) D) 21 43) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 44) (0, ) 44) A) decreasing Answer: C Explanation: B) constant C) increasing A) B) C) Solve the problem. 45) Jacey, a commissioned salesperson, earns $450 base pay plus $37 per item sold. Express Jacey’s gross salary G as a function of the number x of items sold. A) G(x) = 450x +37 B) G(x) = 37x + 450 C) G(x) = 37(x + 450) Answer: B Explanation: 45) D) G(x) = 450(x + 37) A) B) C) D) Solve. 46) A rock falls from a tower that is 400 ft high. As it is falling, its height is given by the formula h(t) = 400 – 16t2 . How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth. A) 25 sec Answer: D Explanation: B) 10,000 sec C) 20 sec A) B) C) D) 22 D) 5 sec 46) Write the equation of a sine function that has the given characteristics. 47) The graph of y = x, shifted 8 units upward A) y = x – 8 B) y = x + 8 C) y = Answer: D Explanation: 47) x-8 D) y = x + 8 A) B) C) D) Use the graph to find the intervals on which it is increasing, decreasing, or constant. 48) 48) A) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) B) Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2) C) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1) D) Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) Answer: A Explanation: A) B) C) D) 23 The graph of a piecewise-defined function is given. Write a definition for the function. 49) 49) A) B) f(x) = 4 x – 4 if -3 x 0 3 2 x 3 f(x) = if 0 x 3 C) 4 x+4 3 if -3 x 0 2 x+2 3 if 0 < x 3 3 x+4 4 if -3 x 0 3 x 2 if 0 < x 3 D) f(x) = Answer: C Explanation: 4 x+4 3 if -3 x 0 2 x 3 if 0 1} C) {x|x -1, 1} Answer: C Explanation: B) {x|x 0} D) all real numbers A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 62) f(x) = -x2 62) A) B) 30 C) Answer: D Explanation: D) A) B) C) D) Graph the function. 63) f(x) = 1 x 63) A) B) 31 C) Answer: B Explanation: D) A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 64) f(x) = (x – 1)2 + 4 64) A) B) 32 C) Answer: A Explanation: D) A) B) C) D) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 65) (- 3, – 3 ) 65) 2 A) constant Answer: C Explanation: B) increasing A) B) C) 33 C) decreasing Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 66) f(x) = x + 80 A) y = ( 82 – 9)x + 82 – 18 B) y = (- 82 + 9)x + C) y = (- 82 – 9)x – 82 + 18 Answer: D Explanation: A) B) C) D) 66) 82 – 18 D) y = ( 82 – 9)x – 82 + 18 Solve the problem. 67) Suppose that the function y = f(x) is decreasing on the interval (7, 3). What can be said about the graph of y = -f(x)? A) decreasing on (7, 3) B) increasing on (7, 3) C) increasing on (-7, -3) Answer: B Explanation: 67) D) decreasing on (-7, -3) A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 68) f(x) = 1 – 2 68) x 34 A) B) C) D) Answer: C Explanation: A) B) C) D) Write the equation of a sine function that has the given characteristics. 69) The graph of y = x , shifted 9 units upward A) y = x – 9 B) y = x – 9 C) y = x + 9 Answer: C Explanation: A) B) C) D) Graph the function. 35 69) D) y = x + 9 70) f(x) = x2 70) A) B) C) D) Answer: D Explanation: A) B) C) D) 36 Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 71) f(x) = x3 – 3×2 + 1; (-5, 5) 71) A) local minimum at (2, -3) B) local maximum at (0, 1) local minimum at (2, -3) D) none C) local minimum at (0, 1) local maximum at (2, -3) Answer: B Explanation: A) B) C) D) Solve the problem. 72) If f(x) = x – B , f(-3) = 0, and f(7) is undefined, what are the values of A and B? 72) x-A A) A = 3, B = -7 Answer: D Explanation: 73) Find f(-x) when f(x) = -x 2 x +5 Answer: A Explanation: C) A = -7, B = 3 D) A = 7, B = -3 A) B) C) D) Find the value for the function. A) B) A = -3, B = 7 x . 2 x +5 B) 73) -x 2 x -5 C) -x -x2 + 5 D) x 2 -x + 5 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 37 74) f(x) = x + 3 + 5 74) A) B) C) D) Answer: A Explanation: A) B) C) D) 38 Determine algebraically whether the function is even, odd, or neither. 75) f(x) = 1 x2 A) even Answer: A Explanation: B) odd 75) C) neither A) B) C) For the function, find the average rate of change of f from 1 to x: f(x) – f(1) ,x 1 x-1 76) f(x) = 2 76) x+1 A) 2 (x – 1)(x + 1) Answer: B Explanation: B) – 1 C) x+1 1 x+1 D) 2 x(x + 1) A) B) C) D) Write the equation that results in the desired transformation. 77) The graph of y = x3 , vertically compressed by a factor of 0.9 A) y = (x + 0.9)3 Answer: C Explanation: B) y = (x – 0.9)3 C) y = 0.9×3 77) D) y = 0.9 x A) B) C) D) Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 78) The reflection of the graph of y = f(x) across the y-axis A) (-2, -4) B) (2, -4) C) (2, 4) D) (-2, 4) Answer: D Explanation: 3 A) B) C) D) 39 78) The graph of a function f is given. Use the graph to answer the question. 79) How often does the line y = -10 intersect the graph? 79) 10 10 -10 -10 A) once C) three times Answer: D Explanation: B) twice D) does not intersect A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 80) f(x) = 1 x3 80) 6 40 A) B) C) D) Answer: C Explanation: A) B) C) D) Answer the question about the given function. 2 81) Given the function f(x) = x – 9 , is the point (1, 5 ) on the graph of f? x+3 2 A) Yes Answer: B Explanation: B) No A) B) 41 81) The graph of a function f is given. Use the graph to answer the question. 82) What are the x-intercepts? 82) 100 100 -100 -100 A) -60, 70 C) -60 Answer: B Explanation: B) -60, 70, 100 D) -100, -60, 70, 100 A) B) C) D) Find and simplify the difference quotient of f, f(x + h) – f(x) , h 0, for the function. h 83) f(x) = 3 83) A) 3 Answer: B Explanation: C) 1 + 6 h B) 0 D) 1 A) B) C) D) Solve the problem. 84) A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A? A) A(x) = -x2 + 400x; {x|0 < x < 400} B) A(x) = -x2 + 400x; {x|0 < x < 800} C) A(x) = x2 + 400x; {x|0 < x < 400} Answer: A Explanation: D) A(x) = -x2 + 800x; {x|0 < x 0 f(x) = C) 3 x+4 4 if -3 x 0 3 x 2 if x 0 4 x+4 3 if -3 x 0 2 x 3 if 0 0 f(x) = A) B) C) D) Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 95) The reflection of the graph of y = f(x) across the x-axis A) (-2, -4) B) (-2, 4) C) (2, 4) D) (2, -4) Answer: D Explanation: A) B) C) D) 48 95) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 96) (-3, 0) 96) A) decreasing Answer: C Explanation: B) constant C) increasing A) B) C) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 97) f(x) = -3(x + 1)2 + 2 97) A) B) 49 C) Answer: C Explanation: D) A) B) C) D) Solve the problem. 98) Find (f – g)(4) when f(x) = 5×2 + 1 and g(x) = x – 4. A) 73 B) 89 Answer: D Explanation: 98) C) -85 D) 81 A) B) C) D) Solve. 99) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 3×2 – 168x + 66, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? A) 33 watches B) 28 watches C) 66 watches D) 30 watches Answer: B Explanation: A) B) C) D) 50 99) Answer the question about the given function. 2 100) Given the function f(x) = x – 8 , if x = -2, what is f(x)? What point is on the graph of f? x+1 A) 4; (-2, 4) Answer: A Explanation: B) – 12; (- 12, -2) C) – 12; (-2, – 12) 100) D) 4; (4, -2) A) B) C) D) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 101) (- 3 , 0) 101) 2 A) constant Answer: C Explanation: B) decreasing C) increasing A) B) C) Solve the problem. 102) A rectangular box with volume 506 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base. Express the cost the box as a function of x. A) C(x) = 2×2 + 4048 B) C(x) = 4x + 4048 x x2 C) C(x) = 3×2 + 4048 D) C(x) = 3×2 + 2024 x Answer: C Explanation: x A) B) C) D) Graph the function. 51 102) 103) f(x) = x 103) A) B) C) D) Answer: C Explanation: A) B) C) D) 52 Solve the problem. 104) Suppose that the x-intercepts of the graph of y = f(x) are 7 and 4. What are the x-intercepts of y = f(x + 3)? A) 10 and 7 B) 21 and 12 C) 4 and 1 D) 7 and 7 Answer: C Explanation: 104) A) B) C) D) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 105) (-1, 1) 105) A) increasing Answer: C Explanation: B) constant C) decreasing A) B) C) 53 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 106) 106) A) function B) function domain: {x|x 0} range: {y|y -2} intercepts: (-2, 0), (0, 2), (2, 0) symmetry: y-axis C) function domain: all real numbers range: all real numbers intercepts: (-2, 0), (0, 2), (2, 0) symmetry: none Answer: B Explanation: domain: {x|x -2} range: {y|y 0} intercepts: (-2, 0), (0, 2), (2, 0) symmetry: none D) not a function A) B) C) D) Determine whether the equation defines y as a function of x. 107) y = 4×2 – 6x + 9 A) function Answer: A Explanation: 107) B) not a function A) B) 54 Solve the problem. 108) A wire of length 7x is bent into the shape of a square. Express the area A of the square as a function of x. A) A(x) = 1 x2 B) A(x) = 49 x2 C) A(x) = 7 x2 D) A(x) = 49 x2 16 8 4 16 Answer: D Explanation: 108) A) B) C) D) Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 109) f(x) = x2 + 2x – 3; (-5, 5) 109) A) local maximum at (-1, 4) C) local minimum at (-1, -4) Answer: C Explanation: B) local minimum at (1, 4) D) local maximum at (1, -4) A) B) C) D) Find the value for the function. 110) Find f(x + h) when f(x) = -5x + 9 . 110) 8x + 3 A) -5x – 5h + 9 8x + 8h + 3 Answer: A Explanation: B) -5x + 9h C) -5x – 5h + 9 8x + 3h 8x + 3 D) -5x + 4h 8x + 11h A) B) C) D) Solve the problem. 111) A retail store buys 250 VCRs from a distributor at a cost of $175 each plus an overhead charge of $ 35 per order. The retail markup is 35% on the total price paid. Find the profit on the sale of one VCR. A) $61.25 B) $61.30 C) $61.20 D) $6130.00 Answer: B Explanation: A) B) C) D) 55 111) 112) From a 48-inch by 48-inch piece of metal, squares are cut out of the four corners so that the sides 112) can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of x. A) V(x) = 2×3 – 144×2 + 48x B) V(x) = 4×3 – 192×2 + 2304x C) V(x) = 4×3 – 192×2 Answer: B Explanation: D) V(x) = 2×3 – 144×2 A) B) C) D) 113) The following graph shows the private, public and total national school enrollment for students for select years from 1970 through 2000. i) How is the graph for total school enrollment, T, determined from the graph of the private enrollment, r, and the public enrollment, u? ii) During which 10-year period did the total number of students enrolled increase the least? iii) During which 10-year period did the total number of students enrolled increase the most? A) i) T is the difference of r and u. B) i) T is the sum of r and u. ii) 1970 – 1980 ii) 1970 – 1980 iii) 1990-2000 iii) 1980-1990 C) i) T is the sum of r and u. D) i) T is the sum of r and u. ii) 1970 – 1980 ii) 1990-2000 iii) 1990-2000 iii) 1970-1980 Answer: C Explanation: A) B) C) D) 56 113) Determine algebraically whether the function is even, odd, or neither. 114) f(x) = 9×3 – 3 A) even Answer: C Explanation: B) odd 114) C) neither A) B) C) For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 115) 115) A) Absolute maximum: f(3) = 6; Absolute minimum: f(0) = 2 B) Absolute maximum: f(3) = 6; Absolute minimum: none C) Absolute maximum: f(7) = 4; Absolute minimum: f(0) = 2 D) Absolute maximum: f(3) = 6; Absolute minimum: f(5) = 1 Answer: B Explanation: A) B) C) D) 57 The graph of a function f is given. Use the graph to answer the question. 116) Find the numbers, if any, at which f has a local minimum. What are the local minima? A) f has a local minimum at x = 0; the local minimum is -2 B) f has a local minimum at x = – ; the local minimum is -2 C) f has a local minimum at x = – and ; the local minimum is 2 D) f has no local minimum Answer: A Explanation: A) B) C) D) 58 116) For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 117) 117) A) Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2 B) Absolute maximum: none; Absolute minimum: f(1) = 2 C) Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2 D) Absolute maximum: none; Absolute minimum: none Answer: B Explanation: A) B) C) D) Determine whether the equation defines y as a function of x. 118) y = ± 1 – 3x A) function Answer: B Explanation: A) B) 59 118) B) not a function The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 119) (-6, -2.5) 119) A) constant Answer: B Explanation: B) decreasing C) increasing A) B) C) Solve the problem. 120) A firm is considering a new product. The accounting department estimates that the total cost, C(x), of 120) producing x units will be C(x) = 85x + 3140. The sales department estimates that the revenue, R(x), from selling x units will be R(x) = 95x, but that no more than 702 units can be sold at that price. Find and interpret (R – C)(702). A) $3880 profit, income exceeds cost B) -$3880 loss, cost exceeds income It is worth it to develop product. It is not worth it to develop product. C) $1016 profit, income exceeds cost D) $129,500 profit, income exceeds cost It is worth it to develop product. It is worth it to develop product. Answer: A Explanation: A) B) C) D) Find the value for the function. 121) Find f(-9) when f(x) = |x|- 6. A) 15 B) -15 Answer: C Explanation: 121) C) 3 A) B) C) D) 60 D) -3 The graph of a function f is given. Use the graph to answer the question. 122) For what numbers x is f(x) < 0? 122) 50 50 -50 -50 A) (- , -30) C) (-30, 35) Answer: C Explanation: B) (-30, ) D) [-50, -30), (35, 50) A) B) C) D) Solve the problem. 123) A rectangle that is x feet wide is inscribed in a circle of radius 19 feet. Express the area of the rectangle as a function of x. A) A(x) = x(1444 -x2 ) B) A(x) = x 1083 – x C) A(x) = x 1444 – x2 Answer: C Explanation: A) B) C) D) D) A(x) = x2 722 – x2 Graph the function. 61 123) 124) 124) f(x) = -x + 3 2x – 3 if x < 2 if x 2 A) B) C) D) Answer: D Explanation: A) B) C) D) 62 Find the function. 125) Find the function that is finally graphed after the following transformations are applied to the graph of y = x . The graph is shifted up 3 units, reflected about the x-axis, and finally shifted right 4 units. A) y = – ,x + 4 – 3 B) y = – ,x – 4 + 3 C) y = – ,x – 4 – 3 D) y = -x + 4 + 3 Answer: B Explanation: A) B) C) D) Determine algebraically whether the function is even, odd, or neither. 126) f(x) = x A) even B) odd Answer: C Explanation: 126) C) neither A) B) C) 3 127) f(x) = -x 127) 9×2 – 5 A) even Answer: B Explanation: B) odd C) neither A) B) C) For the given functions f and g, find the requested function and state its domain. 128) f(x) = x + 11; g(x) = 3 x 128) Find f · g. A) (f · g)(x) = 3x + 33 ; {x|x -11, x 0} x B) (f · g)(x) = C) (f · g)(x) = 14 ; {x|x 0} x D) (f · g)(x) = 3 x + 11 ; {x|x -11, x 0} Answer: D Explanation: 125) 3x + 33 ; {x|x -11, x 0} x x A) B) C) D) 63 Find the value for the function. 129) Find f(x + h) when f(x) = 2×2 + 3x – 4. A) 2×2 + 4xh + 2h2 + 3x + 3h – 4 C) 2×2 + 2xh + 2h2 + 3x + 3h – 4 Answer: A Explanation: 129) B) 2×2 + 2h 2 + 3x + 3h – 4 D) 2×2 + 2h 2 + 7x + 7h – 4 A) B) C) D) Find the function. 130) Find the function that is finally graphed after the following transformations are applied to the graph of y = x. The graph is shifted up 2 units, reflected about the x-axis, and finally shifted left 6 units. A) y = -x – 6 + 2 B) y = – x – 6 – 2 C) y = – x + 6 – 2 D) y = – x + 6 + 2 Answer: D Explanation: A) B) C) D) 64 130) Based on the graph, find the range of y = f(x). 131) 131) f(x) = 4 |x| if -4 x < -2 if -2 x -14} Answer: A Explanation: B) {x|x 0} D) {x|x -14} A) B) C) D) 74 Locate any intercepts of the function. 149) 149) if x 10. Find the approximate number of fish that can be caught if you fish for 30 minutes. A) About 9 fish B) About 32 fish C) About 19 fish D) About 34 fish Answer: A Explanation: 176) A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 177) f(x) = 6|x| 177) A) B) 85 C) Answer: A Explanation: D) A) B) C) D) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 178) (0, 1) 178) A) decreasing Answer: A Explanation: B) constant C) increasing A) B) C) 86 Find the domain of the function. 179) f(x) = x2 + 6 179) A) {x|x -6} C) {x|x -6} Answer: B Explanation: B) all real numbers D) {x|x > -6} A) B) C) D) Solve the problem. 180) Suppose a cold front is passing through the United States at noon with a shape described by the 1 2 function y = x , where each unit represents 100 miles. St. Louis, Missouri is located at (0, 0), and 21 180) the positive y-axis points north. N W E S Suppose the front moves south 340 miles and west 120 miles and maintains its shape. Give the equation for the new front and plot the new position of the front. A) y = 1 (x + 1.2)2 – 3.4 B) y = 1 (x – 1.2)2 – 3.4 21 21 N W N E W S E S 87 C) y = – 1 (x + 1.2)2 – 3.4 D) y = 1 (x – 1.2)2 + 3.4 N N 21 W 21 E W S Answer: A Explanation: E S A) B) C) D) 181) Find f (-2) when f(x) = 5x – 4 and g(x) = 3×2 + 14x + 5. 181) g A) – 3 Answer: C Explanation: C) 14 B) 0 11 11 D) 1 2 A) B) C) D) Determine algebraically whether the function is even, odd, or neither. 182) f(x) = -2×2 + 9 A) even Answer: A Explanation: B) odd 182) C) neither A) B) C) 88 Solve the problem. 183) Suppose that the x-intercepts of the graph of y = f(x) are 8 and 5. What are the x-intercepts of y = 4f(x)? A) 40 and 20 B) 8 and 5 C) 12 and 9 D) 4 and 1 Answer: B Explanation: A) B) C) D) 184) Suppose that the function y = f(x) is increasing on the interval (4, 5). Over what interval is the graph of y = f(x + 2) increasing? A) (2, 3) B) (4, 5) Answer: A Explanation: C) (6, 7) 184) D) (8, 10) A) B) C) D) 185) If f(x) = 9×3 + 2×2 – x + C and f(2) = 1, what is the value of C? A) C = -77 B) C = -29 C) C = 83 Answer: A Explanation: 183) 185) D) C = 67 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 186) f(x) = (-x)2 186) 89 A) B) C) D) Answer: C Explanation: A) B) C) D) For the given functions f and g, find the requested function and state its domain. 187) f(x) = 8 – x; g(x) = x – 1 Find f · g. A) (f · g)(x) = (8 – x)(x – 1); {x|x 0} C) (f · g)(x) = (8 – x)(x – 1); {x|x 1, x 8} Answer: B Explanation: A) B) C) D) B) (f · g)(x) = (8 – x)(x – 1); {x|1 x 8} D) (f · g)(x) = -x2 – 8; {x|x 8} Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 90 187) 188) f(x) = (x – 4)3 188) A) B) C) D) Answer: B Explanation: A) B) C) D) 91 Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. 189) f(x) = x3 – 3×2 + 1, (-1, 3) 189) A) local maximum at (2, -3) B) local maximum at (0, 1) local minimum at (0, 1) increasing on (-1, 0) and (2, 3) decreasing on (0, 2) C) local maximum at (0, 1) local minimum at (2, -3) increasing on (0, 2) decreasing on (-1, 0) and (2, 3) Answer: B Explanation: local minimum at (2, -3) increasing on (-1, 0) and (2, 3) decreasing on (0, 2) D) local maximum at (2, -3) local minimum at (0, 1) increasing on (-1, 0) decreasing on (0, 2) A) B) C) D) The graph of a function f is given. Use the graph to answer the question. 190) Is f(6) positive or negative? 10 10 -10 -10 A) positive Answer: B Explanation: B) negative A) B) 92 190) Find the domain of the function. 191) f(x) = 16 – x A) {x|x 16} Answer: D Explanation: 191) B) {x|x 4} C) {x|x 4} D) {x|x 16} A) B) C) D) Solve. 192) John owns a hotdog stand. His profit is represented by the equation P(x) = -x2 + 10x + 35, with P 192) being profits and x the number of hotdogs sold. What is the most he can earn? A) $60 B) $25 C) $110 D) $35 Answer: A Explanation: A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 193) f(x) = (x + 1)3 – 3 193) A) B) 93 C) D) Answer: B Explanation: A) B) C) D) The graph of a piecewise-defined function is given. Write a definition for the function. 194) 194) A) B) f(x) = x+1 1 x+2 2 if 0 x 3 if 3 < x 5 C) if 0 x 3 f(x) = x+1 1 1 x2 2 if 0 x 3 f(x) = x+1 1 1 x+ 2 2 if 3 < x 5 D) x+1 f(x) = 1 x 2 Answer: D Explanation: if 0 x 3 if 3 < x 5 A) B) C) D) 94 if 3 2} A) B) C) D) 100 Solve the problem. 207) The height s of a ball (in feet) thrown with an initial velocity of 90 feet per second from an initial height of 6 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 90t + 6. What is the 207) maximum height? Round to the nearest hundredth, if necessary. A) 132.56 ft Answer: A Explanation: B) 126.94 ft C) 146.63 ft A) B) C) D) Write the equation that results in the desired transformation. 208) The graph of y = x2 , vertically stretched by a factor of 6 A) y = -6×2 Answer: B Explanation: D) -98.06 ft B) y = 6×2 C) y = (x – 6)2 208) D) y = 6(x – 6)x2 A) B) C) D) Solve the problem. 209) Find (fg)(-2) when f(x) = x + 3 and g(x) = 3×2 + 17x + 3. A) -75 B) -27 C) -19 Answer: C Explanation: A) B) C) D) 101 209) D) 95 210) From April through December 2000, the stock price of QRS Company had a roller coaster ride. 210) The chart below indicates the price of the stock at the beginning of each month during that period. Find the monthly average rate of change in price between June and September. Month Price April (x = 1) 115 May 109 June 89 July 101 August 96 September 113 October 92 November 84 December 64 A) -$8.00 per month B) $12.00 per month C) -$12.00 per month Answer: D Explanation: D) $8.00 per month A) B) C) D) Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 211) y = 4f(x) A) (5, 3) B) (3, 8) C) (8, 4) D) (2, 16) Answer: D Explanation: A) B) C) D) Find the value for the function. 2 212) Find f(x + 1) when f(x) = x – 8 . 212) x-3 2 2 A) x – 7 2 B) x + 2x – 7 x-2 Answer: D Explanation: 211) C) x + 2x + 9 x+4 x-2 A) B) C) D) 102 2 D) x + 2x – 7 x-2 For the given functions f and g, find the requested function and state its domain. 213) f(x) = 3×3 + 2; g(x) = 4×2 + 1 213) Find f · g. A) (f · g)(x) = 12×6 + 3×3 + 8×2 + 2; all real numbers B) (f · g)(x) = 12×5 + 3×3 + 8×2 + 2; all real numbers C) (f · g)(x) = 12×5 + 3×3 + 8×2 + 2; {x|x 0} D) (f · g)(x) = 3×3 + 4×2 + 2; all real numbers Answer: B Explanation: A) B) C) D) Complete the square and then use the shifting technique to graph the function. 214) f(x) = x2 – 3x – 9 A) B) 103 214) C) Answer: D Explanation: D) A) B) C) D) Write the equation of a sine function that has the given characteristics. 215) The graph of y = x, shifted 3 units downward A) y = x + 3 B) y = x + 3 C) y = Answer: C Explanation: A) B) C) D) 104 215) x-3 D) y = x – 3 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 216) 216) A) function B) function domain: all real numbers range: {y|y = 3 or y = 6} intercept: (0, 6) symmetry: none C) function domain: {x|x = 3 or x = 6} range: all real numbers intercept: (6, 0) symmetry: x-axis Answer: D Explanation: domain: all real numbers range: all real numbers intercept: (0, 6) symmetry: none D) not a function A) B) C) D) Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 217) f(x) = x4 – 5×3 + 3×2 + 9x – 3; (-5, 5) 217) A) local minimum at (-0.61, -5.64) B) local minimum at (-0.57, -6.12) local maximum at (1.41, 6.12) local minimum at (3, -3) C) local minimum at (-1, -6) local maximum at (1, 6) local minimum at (3, -3) Answer: B Explanation: local maximum at (1.32, 5.64) local minimum at (3, -3) D) local minimum at (-3, -3) local maximum at (-1.32, 5.64) local minimum at (0.57, -6.12) A) B) C) D) 105 Solve the problem. 218) Sue wants to put a rectangular garden on her property using 76 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the garden’s area as a function of x. A) A(x) = 38x – 1 x2 B) A(x) = 38×2 – x 2 C) A(x) = 37x – 1 x2 D) A(x) = 39x – 2×2 4 Answer: A Explanation: A) B) C) D) The graph of a function f is given. Use the graph to answer the question. 219) How often does the line y = 2 intersect the graph? 10 10 -10 -10 A) once C) three times Answer: C Explanation: 218) B) twice D) does not intersect A) B) C) D) 106 219) Solve the problem. 220) A farmer’s silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is h feet, express the volume of the silo as a function of h. A) V(h) = 100 (h – 10) + 2000 B) V(h) = 100 (h 2 – 10) + 5000 3 3 C) V(h) = 4100 (h – 10) + 500 D) V(h) = 100 h + 4000 h 2 7 Answer: A Explanation: 220) 3 A) B) C) D) Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 221) f(x) = 2 + 8x – x2; (-5, 5) 221) A) local maximum at (4, 18) C) local minimum at (4, 50) Answer: A Explanation: B) local minimum at (-4, 18) D) local maximum at (-4, 50) A) B) C) D) Answer the question about the given function. 2 222) Given the function f(x) = x + 8 , list the y-intercept, if there is one, of the graph of f. x+3 A) ( 8 , 0) B) (0, 8 ) 3 Answer: B Explanation: C) (0, -3) 3 A) B) C) D) 107 D) (0, -8) 222) For the given functions f and g, find the requested function and state its domain. 223) f(x) = 2x + 5; g(x) = 3x – 1 f Find . g 223) A) f (x) = 2x + 5 ; x|x 1 B) f (x) = 3x – 1 ; x|x – 5 C) f (x) = 3x – 1 ; x|x 1 D) f (x) = 2x + 5 ; x|x – 5 g g Answer: A Explanation: 3x – 1 2x + 5 3 g 3 g 2x + 5 3x – 1 2 2 A) B) C) D) Find the value for the function. 224) Find -f(x) when f(x) = 2×2 – 3x + 3. A) 2×2 + 3x – 3 B) 2×2 + 3x + 3 Answer: C Explanation: 224) C) -2×2 + 3x – 3 D) -2×2 + 3x + 3 A) B) C) D) Graph the function. 225) f(x) = x 225) 108 A) B) C) D) Answer: C Explanation: A) B) C) D) Solve the problem. 226) The price p and the quantity x sold of a certain product obey the demand equation: 1 p = – x + 300, {x|0 x 500} 5 What is the revenue to the nearest dollar when 400 units are sold? A) $170,000 B) $152,000 C) $88,000 Answer: C Explanation: A) B) C) D) 109 D) $10,000 226) Use the graph to find the intervals on which it is increasing, decreasing, or constant. 227) 227) A) Increasing on – , – 2 and 2 , ; decreasing on – , 2 2 B) Decreasing on – , 0 ; increasing on 0, C) Increasing on (- , ) D) Decreasing on – , Answer: D Explanation: 2 and 2 , ; increasing on – A) B) C) D) Solve the problem. 228) If f(x) = int(2x), find f(-1.6). A) -4 B) -2 Answer: A Explanation: , 2 2 228) C) -3 D) -1 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 110 229) f(x) = |x + 5| + 2 229) A) B) C) D) Answer: C Explanation: A) B) C) D) 111 230) f(x) = x3 + 3 230) A) B) C) D) Answer: A Explanation: A) B) C) D) Graph the function. 112 231) 231) f(x) = x+5 -5 -x + 4 if -8 x 2 A) B) C) D) Answer: B Explanation: A) B) C) D) 113 For the given functions f and g, find the requested function and state its domain. 232) f(x) = 6x – 9; g(x) = 4x – 2 Find f – g. 232) A) (f – g)(x) = -2x + 7; all real numbers B) (f – g)(x) = 10x – 11; {x|x 1} C) (f – g)(x) = 2x – 7; all real numbers D) (f – g)(x) = 2x – 11; {x|x 11 } Answer: C Explanation: 2 A) B) C) D) Find the average rate of change for the function between the given values. 233) f(x) = 4×2 ; from 0 to 7 4 A) 7 Answer: A Explanation: C) – 3 B) 2 10 233) D) 1 3 A) B) C) D) The graph of a function f is given. Use the graph to answer the question. 234) Use the graph of f given below to find f(-10). 234) 10 10 -10 -10 A) 0 Answer: D Explanation: B) 16 C) -10 A) B) C) D) 114 D) 6 Graph the function. 235) 235) f(x) = -x + 2 x+3 x 0} intercept: (1, 0) symmetry: none C) function domain: {x|x > 0} range: all real numbers intercept: (1, 0) symmetry: none Answer: C Explanation: domain: {x|x > 0} range: all real numbers intercept: (0, 1) symmetry: origin D) not a function A) B) C) D) 124 The graph of a function f is given. Use the graph to answer the question. 254) Is f(40) positive or negative? 254) 50 50 -50 -50 A) positive Answer: A Explanation: B) negative A) B) Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 255) f(x) = x3 + x A) y = 8x – 6 Answer: A Explanation: B) y = -8x – 6 C) y = 8x + 6 A) B) C) D) 125 255) D) y = -8x + 6 Determine whether the relation represents a function. If it is a function, state the domain and range. 256) 256) Alice Brad Carl cat dog A) function domain: {Alice, Brad, Carl} range: {cat, dog} B) function domain: {cat, dog} range: {Alice, Brad, Carl} C) not a function Answer: A Explanation: A) B) C) Solve the problem. 257) Suppose that the function y = f(x) is increasing on the interval (2, 8). Over what interval is the graph of y = f(x – 9) increasing? A) (18 , 72) B) (-7, -1) C) (11, 17) D) (2, 8) Answer: C Explanation: A) B) C) D) 258) Bob wants to fence in a rectangular garden in his yard. He has 66 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x. A) A(x) = 33x – x2 B) A(x) = 35×2 – x C) A(x) = 34x – x2 Answer: A Explanation: 257) D) A(x) = 32x – x2 A) B) C) D) 126 258) The graph of a function is given. Decide whether it is even, odd, or neither. 259) 259) A) even B) odd Answer: A Explanation: C) neither A) B) C) Find the average rate of change for the function between the given values. 260) f(x) = 3 ; from 1 to 4 x+2 A) 1 B) -28 2 Answer: D Explanation: 260) D) – 1 C) -2 6 A) B) C) D) Solve the problem. 261) Given f(x) = 1 and ( f )(x) = x + 6 , find the function g. x g A) g(x) = x + 4 B) g(x) = x – 6 x-6 Answer: D Explanation: 261) x2 – 4x C) g(x) = x + 6 x+4 x-4 A) B) C) D) 127 D) g(x) = x – 4 x+6 262) A box with an open top is to be constructed from a rectangular piece of cardboard with 262) dimensions 12 inches by 25 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. 25 12 A) V(x) = (12 – 2x)(25 – 2x) C) V(x) = (12 – x)(25 – x) Answer: D Explanation: B) V(x) = x(12 – x)(25 – x) D) V(x) = x(12 – 2x)(25 – 2x) A) B) C) D) The graph of a function f is given. Use the graph to answer the question. 263) Find the numbers, if any, at which f has a local minimum. What are the local minima? A) f has a local minimum at x = -2; the local minimum is 0 B) f has a local minimum at x = 0; the local minimum is 1 C) f has a local minimum at x = -2 and 2; the local minimum is 0 D) f has no local minimum Answer: C Explanation: A) B) C) D) 128 263) The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 264) (0, 3) 264) A) increasing Answer: B Explanation: B) constant C) decreasing A) B) C) Solve the problem. 265) A steel can in the shape of a right circular cylinder must be designed to hold 500 cubic centimeters of juice (see figure). It can be shown that the total surface area of the can (including the ends) is 1000 given by S(r) = 2 r2 + , where r is the radius of the can in centimeters. Using the TABLE r feature of a graphing utility, find the radius that minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter. A) 4.3 cm Answer: A Explanation: B) 5.5 cm C) 0 cm A) B) C) D) 129 D) 3.5 cm 265) Answer the question about the given function. 2 266) Given the function f(x) = x + 2 , list the x-intercepts, if any, of the graph of f. x-8 A) (- 2, 0) Answer: D Explanation: B) (2, 0), (-2, 0) C) (8, 0) 266) D) none A) B) C) D) Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. 267) y = 2f(x) A) B) C) D) 130 267) Answer: C Explanation: A) B) C) D) Find the domain of the function. 268) 268) f(x) = 1 |x| if -6 x < -3 if -3 x < 6 x if 6 x 18 A) {x|6 x 18} B) {x|x -6} D) {x|-6 x 18} C) {x|-6 x < 6 or 6 < x 18} Answer: D Explanation: A) B) C) D) Solve the problem. 269) The function f(t) = -0.14t2 + 0.5t + 31.8 models the U.S. population in millions, ages 65 and older, 269) where t represents years after 1990. The function g(t) = 0.54t2 + 12.3t + 106.8 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the g g function represent? Find (5). f f A) Cost per person in thousands of dollars. $5.90 thousand B) Cost per person in thousands of dollars. $0.17 thousand C) Cost per person in thousands of dollars. $12.50 thousand D) Cost per person in thousands of dollars. $0.21 thousand Answer: A Explanation: A) B) C) D) 270) If f(x) = x – 5A and f(10) = -5, what is the value of A? 270) 10x + 2 A) A = -104 Answer: B Explanation: B) A = 104 C) A = -100 A) B) C) D) Graph the function. 131 D) A = 100 271) f(x) = x3 271) A) B) C) D) Answer: B Explanation: A) B) C) D) 132 For the function, find the average rate of change of f from 1 to x: f(x) – f(1) ,x 1 x-1 272) f(x) = x + 48 A) 272) x + 48 + 7 x-1 Answer: D Explanation: B) x + 48 + 7 x+1 C) x + 48 – 7 x+1 D) x + 48 – 7 x-1 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 273) f(x) = -x3 273) A) B) 133 C) Answer: D Explanation: D) A) B) C) D) Find the value for the function. 274) Find -f(x) when f(x) = |x| – 1. A) |-x| + 1 B) -|x| – 1 Answer: C Explanation: 274) C) -|x| + 1 D) |-x| – 1 A) B) C) D) Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 275) f(x) + 4 A) (2, -4) B) (-2, 4) C) (6, 4) D) (2, 8) Answer: D Explanation: A) B) C) D) Answer the question about the given function. 276) Given the function f(x) = -5×2 + 10x – 8, is the point (2, -18) on the graph of f? A) Yes Answer: B Explanation: 275) B) No A) B) 134 276) The graph of a function is given. Decide whether it is even, odd, or neither. 277) 277) A) even Answer: B Explanation: B) odd C) neither A) B) C) Determine whether the relation represents a function. If it is a function, state the domain and range. 278) 278) 3 6 9 12 15 30 45 60 A) function domain:{15, 30, 45, 60} range: {3, 6, 9, 12} Answer: B Explanation: B) function domain: {3, 6, 9, 12} range: {15, 30, 45, 60} C) not a function A) B) C) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 135 279) f(x) = (-x)3 279) A) B) C) D) Answer: A Explanation: A) B) C) D) 136 Determine algebraically whether the function is even, odd, or neither. 280) f(x) = 5×3 A) even Answer: B Explanation: B) odd 280) C) neither A) B) C) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 281) f(x) = 1 x2 281) 5 A) B) C) D) 137 Answer: A Explanation: A) B) C) D) Graph the function. 282) 282) f(x) = x-5 3 if x 0} 296) B) {x|x 0} D) all real numbers C) {x|x -1} Answer: D Explanation: A) B) C) D) 146 The graph of a function is given. Decide whether it is even, odd, or neither. 297) 297) A) even Answer: B Explanation: B) odd C) neither A) B) C) Determine algebraically whether the function is even, odd, or neither. 3 298) f(x) = x A) even B) odd Answer: B Explanation: 298) C) neither A) B) C) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 299) f(x) = -|x| 299) 147 A) B) C) D) Answer: A Explanation: A) B) C) D) 300) f(x) = 1 300) x-5 148 A) B) C) D) Answer: C Explanation: A) B) C) D) 149 Determine whether the relation represents a function. If it is a function, state the domain and range. 301) {(3.11, 5.31), (3.111, -5.3), ( 5 , 0), (1.67, -3)} 3 A) function domain: {3.11, 3.111, 301) 5 , 1.67} 3 range: {5.31, -5.3, 0, -3} B) function domain: {5.31, -5.3, 0, -3} 5 range: {3.11, 3.111, , 1.67} 3 C) not a function Answer: A Explanation: A) B) C) Determine whether the equation defines y as a function of x. 302) y = 1 x A) function Answer: A Explanation: 302) B) not a function A) B) For the given functions f and g, find the requested function and state its domain. 303) f(x) = 7x – 3 ; g(x) = 5x 2x – 5 2x – 5 Find f – g. A) (f – g)(x) = 2x – 3 ; {x|x 0} B) (f – g)(x) = 2x – 3 ; x|x 5 , x 3 2x – 5 2x – 5 C) (f – g)(x) = 12x + 3 ; x|x 5 2x – 5 Answer: D Explanation: 303) 2 D) (f – g)(x) = 2x – 3 ; x|x 5 2 2x – 5 A) B) C) D) 150 2 2 Find the value for the function. 304) Find f(2x) when f(x) = 7×2 – 5x. A) 14×2 – 20x B) 2 7×2 – 5x Answer: C Explanation: 304) C) 28×2 – 10x D) 14×2 – 10x A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 305) f(x) = |x| – 3 305) A) B) C) D) 151 Answer: B Explanation: A) B) C) D) 306) f(x) = x + 5 306) A) B) C) D) Answer: B Explanation: A) B) C) D) 152 Graph the function. 307) 307) f(x) = 1 |x| 3 x if -1 x < 6 if 6 x 0? 312) 10 10 -10 -10 A) [-10, -6), (7, 10) C) (-6, 7) Answer: A Explanation: B) (-6, ) D) (- -6) A) B) C) D) Solve. 313) John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x2 + 54x + 74, with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? A) 23 hotdogs B) 27 hotdogs Answer: B Explanation: C) 47 hotdogs A) B) C) D) 156 D) 28 hotdogs 313) The graph of a piecewise-defined function is given. Write a definition for the function. 314) 314) A) B) f(x) = 1 x 2 if -4 < x < 0 x if 0 < x < 3 f(x) = C) – 1 x 2 if -4 x 0 x if 0 < x 3 -2x x if -4 x 0 if 0 < x 3 D) f(x) = – 1 x 2 x Answer: B Explanation: f(x) = if -4 < x < 0 if 0 < x < 3 A) B) C) D) For the function, find the average rate of change of f from 1 to x: f(x) – f(1) ,x 1 x-1 315) f(x) = x2 – 2x 315) A) x + 1 Answer: D Explanation: B) 1 C) x2 – 2x – 1 x-1 D) x – 1 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 157 316) f(x) = |-x| 316) A) B) C) D) Answer: D Explanation: A) B) C) D) 158 Determine algebraically whether the function is even, odd, or neither. 317) f(x) = 3×4 – x2 A) even Answer: A Explanation: B) odd C) neither A) B) C) Write the equation of a sine function that has the given characteristics. 318) The graph of y = x, shifted 4 units to the left A) y = x + 4 B) y = x – 4 C) y = Answer: C Explanation: 317) 318) x+4 D) y = x – 4 A) B) C) D) Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 319) f(x) = 1 319) 7x A) B) 159 C) Answer: A Explanation: D) A) B) C) D) The graph of a function is given. Decide whether it is even, odd, or neither. 320) 320) A) even Answer: A Explanation: B) odd C) neither A) B) C) 160 Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 321) f(x) = 6 x+5 A) y = 6 x + 1 7 Answer: C Explanation: B) y = 1 x + 4 7 7 321) C) y = – 1 x + 8 3 7 7 D) y = 1 x + 6 7 7 A) B) C) D) Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. 322) y = – 1 f(x) 2 A) B) 161 322) C) D) Answer: A Explanation: A) B) C) D) Based on the graph, find the range of y = f(x). 323) 323) f(x) = 1 x 5 if x 0 4 if x = 0 A) (-10, 10) C) (- , ) Answer: D Explanation: B) (- , 0) or {0} or (0, ) D) (- , 0) or (0, ) A) B) C) D) 162 Determine whether the equation defines y as a function of x. 324) x – 7y = 9 A) function Answer: A Explanation: 324) B) not a function A) B) Locate any intercepts of the function. 325) 325) f(x) = 1 |x| if -9 x < -2 if -2 x < 9 x if 9 x 29 A) (0, 0), (1, 0) Answer: B Explanation: B) (0, 0) C) (0, 0), (0, 1) A) B) C) D) 163 D) none Answer Key Testname: C2 1) B 2) C 3) A 4) D 5) A 6) D 7) D 8) D 9) D 10) D 11) A 12) C 13) C 14) A 15) A 16) d(t) = 1709t 17) A(x) = 1 x3 2 18) local maximum at (0, 0) local minimum at (0.74, -0.33) increasing on (-2, 0) and (0.74, 2) decreasing on (0, 0.74) 19) $27.50 $32.50; 20 if 0 x 100 C(x) = 12.5 + 0.075x if 100 200 20) local maximum at (0, 6) local minimum at (2.67, -3.48) increasing on (-1, 0) and (2.67, 4) decreasing on (0, 2.67) 21) a. R(x) = – 1 x2 + 100x 10 b. c. R(450) = $24,750.00 d. e. 500; $25,000.00 $50.00 164 Answer Key Testname: C2 22) A(x) = 4 3 + 9 x2 – 15 x + 25; {x|0 x 20 } 16 2 3 23) 6.0°C 24) 25) V(s) = 1 s3 6 26) local maximum at (2.34, 1.61) local minimum at (-1.9, -9.82) increasing on (-1.9, 2.34) decreasing on (-4, -1.9) and (2.34, 5) 27) $18.00 $24.25 $65.50 28) local maximum at (0, 5) local minima at (-2.55, 1.17) and (1.05, 4.65) increasing on (-2.55, 0) and (1.05, 2) decreasing on (-4, -2.55) and (0, 1.05) 29) $39.70 $49.69 if 0 x 300 C(x) = 4.93 + 0.11589x -0.266 + 0.13321x if x > 300 30) $25.52 $42.69 if 0 x 25 C(x) = 8.8 + 0.6686x 4.0475 + 0.8587x if x > 25 31) C 32) C 33) D 34) C 35) D 36) C 37) A 38) D 39) B 40) C 165 Answer Key Testname: C2 41) C 42) C 43) D 44) C 45) B 46) D 47) D 48) A 49) C 50) C 51) D 52) A 53) B 54) A 55) C 56) B 57) D 58) A 59) D 60) C 61) C 62) D 63) B 64) A 65) C 66) D 67) B 68) C 69) C 70) D 71) B 72) D 73) A 74) A 75) A 76) B 77) C 78) D 79) D 80) C 81) B 82) B 166 Answer Key Testname: C2 83) B 84) A 85) B 86) A 87) C 88) A 89) D 90) A 91) C 92) B 93) A 94) A 95) D 96) C 97) C 98) D 99) B 100) A 101) C 102) C 103) C 104) C 105) C 106) B 107) A 108) D 109) C 110) A 111) B 112) B 113) C 114) C 115) B 116) A 117) B 118) B 119) B 120) A 121) C 122) C 123) C 124) D 167 Answer Key Testname: C2 125) B 126) C 127) B 128) D 129) A 130) D 131) B 132) A 133) C 134) D 135) A 136) A 137) D 138) B 139) D 140) D 141) B 142) A 143) A 144) A 145) A 146) C 147) C 148) A 149) C 150) D 151) A 152) A 153) D 154) B 155) D 156) C 157) D 158) C 159) D 160) A 161) D 162) A 163) A 164) D 165) A 166) B 168 Answer Key Testname: C2 167) B 168) D 169) D 170) B 171) B 172) A 173) A 174) C 175) B 176) A 177) A 178) A 179) B 180) A 181) C 182) A 183) B 184) A 185) A 186) C 187) B 188) B 189) B 190) B 191) D 192) A 193) B 194) D 195) B 196) A 197) C 198) C 199) B 200) D 201) D 202) D 203) B 204) D 205) D 206) D 207) A 208) B 169 Answer Key Testname: C2 209) C 210) D 211) D 212) D 213) B 214) D 215) C 216) D 217) B 218) A 219) C 220) A 221) A 222) B 223) A 224) C 225) C 226) C 227) D 228) A 229) C 230) A 231) B 232) C 233) A 234) D 235) A 236) C 237) A 238) C 239) A 240) A 241) C 242) B 243) D 244) A 245) C 246) B 247) B 248) D 249) B 250) D 170 Answer Key Testname: C2 251) C 252) A 253) C 254) A 255) A 256) A 257) C 258) A 259) A 260) D 261) D 262) D 263) C 264) B 265) A 266) D 267) C 268) D 269) A 270) B 271) B 272) D 273) D 274) C 275) D 276) B 277) B 278) B 279) A 280) B 281) A 282) A 283) B 284) C 285) C 286) C 287) D 288) C 289) A 290) C 291) B 292) C 171 Answer Key Testname: C2 293) C 294) A 295) D 296) D 297) B 298) B 299) A 300) C 301) A 302) A 303) D 304) C 305) B 306) B 307) A 308) A 309) B 310) A 311) B 312) A 313) B 314) B 315) D 316) D 317) A 318) C 319) A 320) A 321) C 322) A 323) D 324) A 325) B 172