AnswersFL-1200330-Algebra 2 Sem 1 - FlexComposition of Functions

Comparing a Function and Its Inverse Answers

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1
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Consider the tables that represent ordered pairs corresponding to a function and its inverse.

Question illustration
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.
2
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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
3

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

Question illustration
A
(20, 20)
B
(52, 20)
C
(20, 52)
D
(52, 52)
4

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.
5

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.

Question illustration
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.
6

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

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Option A
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Option
Option B
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Option C
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Option
Option D
7

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?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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

Question illustration
A
–16
B
–12
C
Option
Option C
D
Option
Option D
10

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

Question illustration
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.
11

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?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

The graph below shows two linear functions.

Question illustration
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.
13

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

Question illustration
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.
14

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

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

Question illustration
A
–16
B
–12
C
Option
Option C
D
Option
Option D
17

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
18

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.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
19

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

Question illustration
A
(20, 20)
B
(52, 20)
C
(20, 52)
D
(52, 52)
20

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

Question illustration
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).

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