AnswersFL-1200330-Algebra 2 Sem 1 - FlexFunction Inverses

Comparing a Function and Its Inverse Answers

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Table A represents the function that models the stopping distance in feet of a derby car, d(x), based on the velocity in miles per hour of the car, x.Table B represents the function that models the velocity of a car, v(d), in miles per hour based on distance in feet it took the car to stop, d.

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A
Since the functions in both tables are increasing, they are inverses.
B
Since the functions in both tables are increasing, they are not inverses.
C
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are inverses.
D
Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are not inverses.
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Students are asked to graph the inverse, f–1(x) of an absolute value function, f(x) after restricting its domain. The directions also ask that the graph include a dashed line that can be used to verify that the functions are inverses of each other.Which student’s work is correct?

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3

Consider the tables that represent ordered pairs corresponding to a function and its inverse.

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A
According to the tables, f(x) does not have a y-intercept.
B
According to the tables, f–1(x) does not have an x-intercept.
C
The domain of f(x) is restricted such that x ≥ 0, so the domain of f–1(x) is restricted such that y ≥ 0.
D
The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.
4

Consider the tables that represent a continuous function and its inverse.

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A
The reciprocal of the slope of f(x) is the same as the slope of f–1(x).
B
The negative reciprocal of the slope of f(x) is the same as the slope of f–1(x).
C
The y-coordinate of the y-intercept of f(x) is the same as the y-coordinate of the y-intercept of f–1(x).
D
The opposite of the y-coordinate of the y-intercept of f(x) is the same as the x-coordinate of the x-intercept of f–1(x).
5

Consider the function.What is the y-intercept of f–1(x)?

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–16
B
–12
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6

Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.

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7

A function and its inverse are shown on the graph.

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A
f(x) domain: x ≥ 1f–1(x) domain: x ≥ 1
B
f(x) domain: x ≥ 1f–1(x) range: y ≥ 1
C
f(x) domain: x ≤ –2f–1(x) domain: x ≤ –2
D
f(x) domain: x ≤ –2f–1(x) range: y ≤ –2
8

Consider the function and its inverse. and When comparing the functions using the equations, which conclusion can be made?

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A
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≥ 0.
B
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≤ 0.
C
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≥ 4.
D
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≤ 4.
9

A function and its inverse are shown on the graph.

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A
The range of both f(x) and f–1(x) is all real numbers.
B
The domain of both f(x) and f–1(x) is all real numbers.
C
The range of f(x) is y > 0 and the domain of f–1(x) is x > 0.
D
The domain of f(x) is x > 0 and the range of f–1(x) is y > 0.
10

The cost table shows the average cost, a(x), of producing x number of earbuds.

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(20, 20)
B
(52, 20)
C
(20, 52)
D
(52, 52)
11

Which answer includes a function, its inverse, and a dashed line that verifies the relationship?

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12

Consider the tables created with Fahrenheit and Celsius temperatures. Table A represents the function that models Celsius temperature, C(F), based on the given Fahrenheit temperature, F.

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13

Consider this function.f(x) = |x – 4| + 6If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

A
Since the domain of the original function is limited to x 6, the range of the inverse function is y ≤ 6.
Option A
B
Since the domain of the original function is limited to x 4, the range of the inverse function is y ≤ 1.
Option B
C
Since the range of the original function is limited to y 6, the domain of the inverse function is x ≥ 6.
Option C
D
Since the range of the original function is limited to y 4, the domain of the inverse function is x ≥ 1.
Option D
14

A linear function and its inverse are given. Which tables could be used to verify that the functions are inverses of each other? Select two options.

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15

The graph below shows two linear functions.

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A
Neither of the lines is parallel to the line y = x; therefore, the functions are inverses of each other.
B
Neither of the lines is parallel to the line y = x; therefore, the functions are not inverses of each other.
C
The point of intersection of the two functions is not on the line y = x; therefore, the functions are inverses of each other.
D
The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.

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