You used set notation to denote elements, subsets, and complements. (Lesson 0-1)
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1 You used set notation to denote elements, subsets, and complements. (Lesson 0-1) Describe subsets of real numbers. Identify and evaluate functions and state their domains.
2 set-builder notation interval notation function function notation independent variable dependent variable implied domain piecewise-defined function relevant domain
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4 Use Set-Builder Notation A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation. B. Describe x > 17 using set-builder notation. C. Describe all multiples of seven using set-builder notation.
5 Describe {6, 7, 8, 9, 10, } using set-builder notation. A. B. C. D.
6 Use Interval Notation A. Write 2 x 12 using interval notation. B. Write x > 4 using interval notation. C. Write x < 3 or x 54 using interval notation.
7 Write x > 5 or x < 1 using interval notation. A. B. C. ( 1, 5) D.
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10 Identify Relations that are Functions A. Determine whether the relation represents y as a function of x. The input value x is the height of a student in inches, and the output value y is the number of books that the student owns.
11 Identify Relations that are Functions B. Determine whether the table represents y as a function of x.
12 Identify Relations that are Functions C. Determine whether the graph represents y as a function of x.
13 Identify Relations that are Functions D. Determine whether x = 3y 2 represents y as a function of x.
14 Determine whether 12x 2 + 4y = 8 represents y as a function of x. A. Yes; there is exactly one y-value for each x-value. B. No; there is more than one y-value for an x-value.
15 Find Function Values A. If f (x) = x 2 2x 8, find f (3). B. If f (x) = x 2 2x 8, find f ( 3d). C. If f (x) = x 2 2x 8, find f (2a 1).
16 If, find f (6). A. B. C. D.
17 Find Domains Algebraically A. State the domain of the function.
18 Find Domains Algebraically B. State the domain of the function.
19 Find Domains Algebraically C. State the domain of the function.
20 State the domain of g (x) =. A. or [4, ) B. or [ 4, 4] C. or (, 4] D.
21 A. FINANCE Realtors in a metropolitan area studied the average home price per square foot as a function of total square footage. Their evaluation yielded the following piecewisedefined function. Find the average price per square foot for a home with the square footage of 1400 square feet. Evaluate a Piecewise-Defined Function
22 B. FINANCE Realtors in a metropolitan area studied the average home price per square foot as a function of total square footage. Their evaluation yielded the following piecewise-defined function. Find the average price per square foot for a home with the square footage of 3200 square feet. Evaluate a Piecewise-Defined Function
23 ENERGY The cost of residential electricity use can be represented by the following piecewise function, where k is the number of kilowatts. Find the cost of electricity for 950 kilowatts. A. $47.50 B. $48.00 C. $57.50 D. $76.50
24 You identified functions. (Lesson 1-1) Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and zeros of functions. Explore symmetries of graphs, and identify even and odd functions.
25 zeros roots line symmetry point symmetry even function odd function
26 Estimate Function Values A. ADVERTISING The function f (x) = 5x x approximates the profit at a toy company, where x represents marketing costs and f (x) represents profit. Both costs and profits are measured in tens of thousands of dollars. Use the graph to estimate the profit when marketing costs are $30,000. Confirm your estimate algebraically.
27 Estimate Function Values B. ADVERTISING The function f (x) = 5x x approximates the profit at a toy company, where x represents marketing costs and f (x) represents profit. Both costs and profits are measured in tens of thousands of dollars. Use the graph to estimate marketing costs when the profit is $1,250,000. Confirm your estimate algebraically.
28 PROFIT A-Z Toy Boat Company found the average price of its boats over a six month period. The average price for each boat can be represented by the polynomial function p (x) = 0.325x x2 + 22, where x is the month, and 0 < x 6. Use the graph to estimate the average price of a boat in the fourth month. Confirm you estimate algebraically. A. B. C. D. $25 $23 $22 $20
29 Find Domain and Range Use the graph of f to find the domain and range of the function.
30 Use the graph of f to find the domain and range of the function. A. Domain: Range: B. Domain: Range: C. Domain: Range: D. Domain: Range:
31 Find y-intercepts A. Use the graph of the function f (x) = x 2 4x + 4 to approximate its y-intercept. Then find the y-intercept algebraically.
32 Find y-intercepts B. Use the graph of the function g (x) = x to approximate its y-intercept. Then find the y-intercept algebraically.
33 Use the graph of the function to approximate its y-intercept. Then find the y-intercept algebraically. A. 1; f (0) = 1 B. 0; f (0) = 0 C. 1; f (0) = 1 D. 2; f (0) = 2
34 Find Zeros Use the graph of f (x) = x 3 x to approximate its zero(s). Then find its zero(s) algebraically.
35 Use the graph of to approximate its zero(s). Then find its zero(s) algebraically. A. 2.5 B. 1 C. 5 D. 9
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37 Test for Symmetry A. Use the graph of the equation y = x to test for symmetry with respect to the x-axis, the y-axis, and the origin. Support the answer numerically. Then confirm algebraically.
38 Test for Symmetry B. Use the graph of the equation xy = 6 to test for symmetry with respect to the x-axis, the y-axis, and the origin. Support the answer numerically. Then confirm algebraically.
39 Use the graph of the equation y = x 3 to test for symmetry with respect to the x-axis, the y-axis, and the origin. Support the answer numerically. Then confirm algebraically. A. symmetric with respect to the x-axis B. symmetric with respect to the y-axis C. symmetric with respect to the origin D. not symmetric with respect to the x-axis, y-axis, or the origin
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41 Identify Even and Odd Functions A. Graph the function f (x) = x 2 4x + 4 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.
42 Identify Even and Odd Functions B. Graph the function f (x) = x 2 4 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.
43 Identify Even and Odd Functions C. Graph the function f (x) = x 3 3x 2 x + 3 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.
44 Graph the function f (x) = x 4 8 using a graphing calculator. Analyze the graph to determine whether the graph is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function. A. odd; symmetric with respect to the origin B. even; symmetric with respect to the y-axis C. neither even nor odd
45 You found domain and range using the graph of a function. (Lesson 1-2) Use limits to determine the continuity of a function, and apply the Intermediate Value Theorem to continuous functions. Use limits to describe end behavior of functions.
46 continuous function limit discontinuous function infinite discontinuity jump discontinuity removable discontinuity nonremovable discontinuity end behavior
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50 Identify a Point of Continuity Determine whether is continuous at. Justify using the continuity test.
51 Determine whether the function f (x) = x 2 + 2x 3 is continuous at x = 1. Justify using the continuity test. A. continuous; f (1) B. Discontinuous; the function is undefined at x = 1 because does not exist.
52 Identify a Point of Discontinuity A. Determine whether the function is continuous at x = 1. Justify using the continuity test. If discontinuous, identify the type of discontinuity as infinite, jump, or removable.
53 Identify a Point of Discontinuity B. Determine whether the function is continuous at x = 2. Justify using the continuity test. If discontinuous, identify the type of discontinuity as infinite, jump, or removable.
54 Determine whether the function is continuous at x = 1. Justify using the continuity test. If discontinuous, identify the type of discontinuity as infinite, jump, or removable. A. B. C. D. f (x) is continuous at x = 1. infinite discontinuity jump discontinuity removable discontinuity
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56 Approximate Zeros A. Determine between which consecutive integers the real zeros of are located on the interval [ 2, 2]. Investigate function values on the interval [ 2, 2].
57 Approximate Zeros B. Determine between which consecutive integers the real zeros of f (x) = x 3 + 2x + 5 are located on the interval [ 2, 2]. Investigate function values on the interval [ 2, 2].
58 A. Determine between which consecutive integers the real zeros of f (x) = x 3 + 2x 2 x 1 are located on the interval [ 4, 4]. A. 1 < x < 0 B. 3 < x < 2 and 1 < x < 0 C. 3 < x < 2 and 0 < x < 1 D. 3 < x < 2, 1 < x < 0, and 0 < x < 1
59 B. Determine between which consecutive integers the real zeros of f (x) = 3x 3 2x are located on the interval [ 2, 2]. A. 2 < x < 1 B. 1 < x < 0 C. 0 < x < 1 D. 1 < x < 2
60 Graphs that Approach Infinity Use the graph of f(x) = x 3 x 2 4x + 4 to describe its end behavior. Support the conjecture numerically.
61 Use the graph of f (x) = x 3 + x 2 2x + 1 to describe its end behavior. Support the conjecture numerically. A. B. C. D.
62 Graphs that Approach a Specific Value Use the graph of to describe its end behavior. Support the conjecture numerically.
63 Use the graph of to describe its end behavior. Support the conjecture numerically. A. B. C. D.
64 Apply End Behavior PHYSICS The symmetric energy function is. If the y-value is held constant, what happens to the value of symmetric energy when the x-value approaches negative infinity? We are asked to describe the end behavior of E (x) for small values of x when y is held constant. That is, we are asked to find.
65 PHYSICS The illumination E of a light bulb is given by, where I is the intensity and d is the distance in meters to the light bulb. If the intensity of a 100-watt bulb, measured in candelas (cd), is 130 cd, what happens to the value of E when the d-value approaches infinity? A. C. B. D.
66 You found function values. (Lesson 1-1) Determine intervals on which functions are increasing, constant, or decreasing, and determine maxima and minima of functions. Determine the average rate of change of a function.
67 increasing decreasing constant maximum minimum extrema average rate of change secant line
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69 Analyze Increasing and Decreasing Behavior A. Use the graph of the function f (x) = x 2 4 to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
70 Analyze Increasing and Decreasing Behavior B. Use the graph of the function f (x) = x 3 + x to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
71 Use the graph of the function f (x) = 2x 2 + 3x 1 to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically. A. f (x) is increasing on (, 1) and ( 1, ). B. f (x) is increasing on (, 1) and decreasing on ( 1, ). C. f (x) is decreasing on (, 1) and increasing on ( 1, ). D. f (x) is decreasing on (, 1) and decreasing on ( 1, ).
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73 Estimate and Identify Extrema of a Function Estimate and classify the extrema to the nearest 0.5 unit for the graph of f (x). Support the answers numerically.
74 Estimate and classify the extrema to the nearest 0.5 unit for the graph of f (x). Support the answers numerically. A. There is a relative minimum of 2 at x = 1 and a relative maximum of 1 at x = 0. There are no absolute extrema. B. There is a relative maximum of 2 at x = 1 and a relative minimum of 1 at x = 0. There are no absolute extrema. C. There is a relative maximum of 2 at x = 1 and no relative minimum. There are no absolute extrema. D. There is no relative maximum and there is a relative minimum of 1 at x = 0. There are no absolute extrema.
75 Use a Graphing Calculator to Approximate Extrema GRAPHING CALCULATOR Approximate to the nearest hundredth the relative or absolute extrema of f (x) = x 4 5x 2 2x + 4. State the x-value(s) where they occur. f (x) = x 4 5x 2 2x + 4 Graph the function and adjust the window as needed so that all of the graph s behavior is visible.
76 GRAPHING CALCULATOR Approximate to the nearest hundredth the relative or absolute extrema of f (x) = x 3 + 2x 2 x 1. State the x-value(s) where they occur. A. relative minimum: (0.22, 1.11); relative maximum: ( 1.55, 1.63) B. relative minimum: ( 1.55, 1.63); relative maximum: (0.22, 1.11) C. relative minimum: (0.22, 1.11); relative maximum: none D. relative minimum: (0.22, 0); relative minimum: ( 0.55, 0) relative maximum: ( 1.55, 1.63)
77 Use Extrema for Optimization FUEL ECONOMY Advertisements for a new car claim that a tank of gas will take a driver and three passengers about 360 miles. After researching on the Internet, you find the function for miles per tank of gas for the car is f (x) = 0.025x x + 240, where x is the speed in miles per hour. What speed optimizes the distance the car can travel on a tank of gas? How far will the car travel at that optimum speed?
78 VOLUME A square with side length x is cut from each corner of a rectangle with dimensions 8 inches by 12 inches. Then the figure is folded to form an open box, as shown in the diagram. Determine the length and width of the box that will allow the maximum volume. A in. by in. B in. by 8.86 in. C. 3 in. by 7 in. D in. by 67.6 in.
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80 Find Average Rates of Change A. Find the average rate of change of f (x) = 2x 2 + 4x + 6 on the interval [ 3, 1].
81 Find Average Rates of Change B. Find the average rate of change of f (x) = 2x 2 + 4x + 6 on the interval [2, 5].
82 Find the average rate of change of f (x) = 3x 3+ 2x + 3 on the interval [ 2, 1]. A. 27 B. 11 C. D. 19
83 Find Average Speed A. GRAVITY The formula for the distance traveled by falling objects on the Moon is d (t) = 2.7t 2, where d (t) is the distance in feet and t is the time in seconds. Find and interpret the average speed of the object for the time interval of 1 to 2 seconds.
84 Find Average Speed B. GRAVITY The formula for the distance traveled by falling objects on the Moon is d (t) = 2.7t 2, where d (t) is the distance in feet and t is the time in seconds. Find and interpret the average speed of the object for the time interval of 2 to 3 seconds.
85 PHYSICS Suppose the height of an object dropped from the roof of a 50 foot building is given by h (t) = 16t , where t is the time in seconds after the object is thrown. Find and interpret the average speed of the object for the time interval 0.5 to 1 second. A. B. C. D. 8 feet per second 12 feet per second 24 feet per second 132 feet per second
86 You analyzed graphs of functions. (Lessons 1-2 through 1-4) Identify, graph, and describe parent functions. Identify and graph transformations of parent functions
87 parent function absolute value function constant function step function zero function greatest integer function identity function transformation quadratic function translation cubic function reflection square root function dilation reciprocal function
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92 Describe Characteristics of a Parent Function Describe the following characteristics of the graph of the parent function : domain, range, intercepts, symmetry, continuity, end behavior, and intervals on which the graph is increasing/decreasing.
93 Describe the following characteristics of the graph of the parent function f (x) = x 2: domain, range, intercepts, symmetry, continuity, end behavior, and intervals on which the graph is increasing/decreasing.
94 A. D:, R: ; y-intercept = (0, 0). The graph is symmetric with respect to the y-axis. The graph is continuous everywhere. The end behavior is as, and as,. The graph is decreasing on the interval and increasing on the interval. B. D:, R: ; y-intercept = (0, 0). The graph is symmetric with respect to the y-axis. The graph is continuous everywhere. The end behavior is as,. As,. The graph is decreasing on the interval and increasing on the interval. C. D:, R: ; y-intercept = (0, 0). The graph is symmetric with respect to the y-axis. The graph is continuous everywhere. The end behavior is as,. As,. The graph is decreasing on the interval and increasing on the interval. D. D:, R: ; no intercepts. The graph is symmetric with respect to the y-axis. The graph is continuous everywhere. The end behavior is as,. As,. The graph is decreasing on the interval and increasing on the interval.
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96 Graph Translations A. Use the graph of f (x) = x 3 to graph the function g (x) = x 3 2.
97 Graph Translations B. Use the graph of f (x) = x 3 to graph the function g (x) = (x 1)3.
98 Graph Translations C. Use the graph of f (x) = x 3 to graph the function g (x) = (x 1)3 2.
99 Use the graph of f (x) = x 2 to graph the function g (x) = (x 2)2 1. A. C. B. D.
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101 Write Equations for Transformations A. Describe how the graphs of and g (x) are related. Then write an equation for g (x).
102 Write Equations for Transformations B. Describe how the graphs of and g (x) are related. Then write an equation for g (x).
103 Describe how the graphs of f (x) = x 3 and g (x) are related. Then write an equation for g (x). A. B. C. D. The graph is translated 3 units up; g (x) = x The graph is translated 3 units down; g (x) = x 3 3. The graph is reflected in the x-axis; g (x) = x 3. The graph is translated 3 units down and reflected in the x-axis; g (x) = x 3 3.
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105 Describe and Graph Transformations A. Identify the parent function f (x) of, and describe how the graphs of g (x) and f (x) are related. Then graph f (x) and g (x) on the same axes.
106 Describe and Graph Transformations B. Identify the parent function f (x) of g (x) = 4x, and describe how the graphs of g (x) and f (x) are related. Then graph f (x) and g (x) on the same axes.
107 Identify the parent function f (x) of g (x) = (0.5x)3, and describe how the graphs of g (x) and f (x) are related. Then graph f (x) and g (x) on the same axes.
108 A. f (x) = x 3; g(x) is f (x) = x 3; g(x) represented by is represented the expansion of by the reflection the graph of f (x) of the graph of f horizontally by a (x) in the x-axis. factor of B. C.. f (x) = x 3; g(x) is D. f (x) = x 2; g(x) is represented by represented by the expansion of the expansion of the graph of the graph of f (x) horizontally f (x) horizontally by a factor of by a factor of and reflected and reflected in the x-axis. in the x-axis.
109 Graph a Piecewise-Defined Function Graph.
110 Graph the function A. C. B. D..
111 Transformations of Functions A. AMUSEMENT PARK The Wild Ride roller coaster has a section that is shaped like the function, where g (x) is the vertical distance in yards the roller coaster track is from the ground and x is the horizontal distance in yards from the start of the ride. Describe the transformations of the parent function f (x) = x 2 used to graph g (x).
112 Transformations of Functions B. AMUSEMENT PARK The Wild Ride roller coaster has a section that is shaped like the function, where g (x) is the vertical distance in yards the roller coaster track is from the ground and x is the horizontal distance in yards from the start of the ride. Suppose the ride designers decide to increase the highest point of the ride to 70 yards. Rewrite g (x) to reflect this change. Graph both functions on the same coordinate axes using a graphing calculator.
113 STUNT RIDING A stunt motorcyclist jumps from ramp to ramp according to the model shaped like the function, where g (x) is the vertical distance in feet the motorcycle is from the ground and x is the horizontal distance in feet from the start of the jump. Describe the transformations of f (x) = x 2 used to graph g (x).
114 A. The graph of g (x) is the graph of f (x) translated 75 units right. B. The graph of g (x) is the graph of f (x) translated 18 units up, compressed vertically, and reflected in the x-axis. C. The graph of g (x) is the graph of f (x) translated 75 units right and reflected in the x-axis. D. The graph of g (x) is the graph of f (x) translated 75 units right and 18 units up, compressed vertically, and reflected in the xaxis.
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116 Describe and Graph Transformations A. Use the graph of f (x) = x 2 4x + 3 to graph the function g(x) = f (x).
117 Describe and Graph Transformations B. Use the graph of f (x) = x 2 4x + 3 to graph the function h (x) = f ( x ).
118 Use the graph of f (x) shown to graph g(x) = f (x) and h (x) = f ( x ).
119 A. C. B. D.
120 You evaluated functions. (Lesson 1-1) Perform operations with functions. Find compositions of functions.
121 composition
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123 Operations with Functions A. Given f (x) = x 2 2x, g (x) = 3x 4, and h (x) = 2x 2 + 1, find the function and domain for (f + g)(x).
124 Operations with Functions B. Given f (x) = x 2 2x, g (x) = 3x 4, and h (x) = 2x 2 + 1, find the function and domain for (f h)(x).
125 Operations with Functions C. Given f (x) = x 2 2x, g(x) = 3x 4, and h (x) = 2x 2 + 1, find the function and domain for (f g)(x).
126 Operations with Functions D. Given f (x) = x 2 2x, g (x) = 3x 4, and h (x) = 2x 2 + 1, find the function and domain for
127 Find (f + g)(x), (f g)(x), (f g)(x), and for 2 f (x) = x + x, g (x) = x 3. State the domain of each new function.
128 A. B. C. D.
129
130 Compose Two Functions A. Given f (x) = 2x 2 1 and g (x) = x + 3, find [f g](x).
131 Compose Two Functions B. Given f (x) = 2x 2 1 and g (x) = x + 3, find [g f](x).
132 Compose Two Functions C. Given f (x) = 2x 2 1 and g (x) = x + 3, find [f g](2).
133 Find for f (x) = 2x 3 and g (x) = 4 + x A. 2x + 11; 4x 12x + 13; B. 2x + 11; 4x 12x + 5; C. 2x + 5; 4x 12x + 5; D. 2x + 5; 4x 12x + 13; 23
134 A. Find. Find a Composite Function with a Restricted Domain
135 B. Find f g. Find a Composite Function with a Restricted Domain
136 Find f g. A. D = (, 1) ( 1, 1) (1, ); B. D = [ 1, 1]; C. D = (, 1) ( 1, 1) (1, ); D. D = (0, 1);
137 Decompose a Composite Function A. Find two functions f and g such that when. Neither function may be the identity function f (x) = x.
138 Decompose a Composite Function B. Find two functions f and g such that when h (x) = 3x 2 12x Neither function may be the identity function f (x) = x.
139 A. B. C. D.
140 Compose Real-World Functions A. COMPUTER ANIMATION An animator starts with an image of a circle with a radius of 25 pixels. The animator then increases the radius by 10 pixels per second. Find functions to model the data.
141 Compose Real-World Functions B. COMPUTER ANIMATION An animator starts with an image of a circle with a radius of 25 pixels. The animator then increases the radius by 10 pixels per second. Find A R. What does the function represent?
142 Compose Real-World Functions C. COMPUTER ANIMATION An animator starts with an image of a circle with a radius of 25 pixels. The animator then increases the radius by 10 pixels per second. How long does it take for the circle to quadruple its original size?
143 BUSINESS A satellite television company offers a 20% discount on the installation of any satellite television system. The company also advertises $50 in coupons for the cost of equipment. Find [c d](x) and [d c](x). Which composition of the coupon and discount results in the lower price? Explain. A. [c d](x) = 0.80x 40; [d c](x) = 0.80x 50; Sample answer: [d c](x) represents the cost of installation using the coupon and then the discount results in the lower cost. B. [c d](x) = 0.80x 40; [d c](x) = 0.80x 50; Sample answer: [c d](x) represents the cost of installation using the discount and then the coupon results in the lower cost. C. [c d](x) = 0.80x 50; [d c](x) = 0.80x 40; Sample answer: [c d](x) represents the cost of installation using the discount and then the coupon results in the lower cost. D. [c d](x) = 0.80x 50; [d c](x) = 0.80x 40; Sample answer: [c d](x) represents the cost of installation using the coupon and then the discount results in the lower cost.
144 You found the composition of two functions. (Lesson 1-6) Use the graphs of functions to determine if they have inverse functions. Find inverse functions algebraically and graphically.
145 inverse relation inverse function one-to-one
146
147 Apply the Horizontal Line Test A. Graph the function f (x) = 4x 2 + 4x + 1 using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no.
148 Apply the Horizontal Line Test B. Graph the function f (x) = x 5 + x 3 1 using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no.
149 Graph the function using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no. C. no A. yes B. yes D. no
150
151 Find Inverse Functions Algebraically A. Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain.
152 Find Inverse Functions Algebraically B. Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain.
153 Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain. A. B. C. D. f 1(x) does not exist.
154
155 Verify Inverse Functions
156 Show that f (x) = x 2 2, x 0 and are inverses of each other. A. B. C. D.
157 Find Inverse Functions Graphically Use the graph of relation A to sketch the graph of its inverse.
158 Use the graph of the function to graph its inverse function. A. C. B. D.
159 Use an Inverse Function A. MANUFACTURING The fixed costs for manufacturing one type of stereo system are $96,000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96, x. Explain why the inverse function f 1(x) exists. Then find f 1(x).
160 Use an Inverse Function B. MANUFACTURING The fixed costs for manufacturing one type of stereo system are $96,000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f (x) = 96, x. What do f 1(x) and x represent in the inverse function?
161 Use an Inverse Function C. MANUFACTURING The fixed costs for manufacturing one type of stereo system are $96,000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f (x) = 96, x. What restrictions, if any, should be placed on the domain of f (x) and f 1(x)? Explain.
162 Use an Inverse Function D. MANUFACTURING The fixed costs for manufacturing one type of stereo system are $96,000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f (x) = 96, x. Find the number of stereos made if the total cost was $216,000.
163 EARNINGS Ernesto earns $12 an hour and a commission of 5% of his total sales as a salesperson. His total earnings f (x) for a week in which he worked 40 hours and had a total sales of $x is given by f (x) = x. Explain why the inverse function f 1(x) exists. Then find f 1(x).
164 A. B. C. D.
Test 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
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