Comparing a Function and Its Inverse

Question 1

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

Revolt · Accepted Answer

The range of f(x) includes values such that y ≥ 1, so the domain of f–1(x) includes values such that x ≥ 1.

Question 2

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?

Revolt · Accepted Answer

Since the range of the original function is limited to y 6, the domain of the inverse function is x ≥ 6.

Question 3

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

Revolt · Accepted Answer

(52, 20)

Question 4

A function and its inverse are shown on the graph.

Revolt · Accepted Answer

The range of f(x) is y > 0 and the domain of f–1(x) is x > 0.

Question 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.

Revolt · Accepted Answer

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.

Question 6

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

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/evresources/597d69572e6817a15a5f7870ebb9282c.png

Question 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?

Revolt · Accepted Answer

Answer image: https://r19.core.learn.edgenuity.com//media.edgenuity.com/evresources/8102/8102-07/8102-07-05/8102-07-05-assessment/8102-07-05-20b.jpg

Question 8

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

Revolt · Accepted Answer

Answer image: https://r19.core.learn.edgenuity.com//media.edgenuity.com/evresources/8102/8102-07/8102-07-05/8102-07-05-assessment/8102-07-05-25a.jpg

Question 9

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

Revolt · Accepted Answer

–16

Question 10

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

Revolt · Accepted Answer

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

Comparing a Function and Its Inverse Answers

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