# Worksheet: Graphs of Inverses of Functions

In this worksheet, we will practice using a graph to find the inverse of a function and analyzing the graphs for the inverse of a function.

Q1:

The following is the graph of .

Which one is the graph of the inverse function ?

• A(b)
• B(a)
• C(c)

Q2:

Liam is looking for an inverse to . He starts with the parabola . He then reflects this in the line to get the shown parabola .

Complete Liam’s work by determining the inverse whose graph is the given solid curve.

• A
• B
• C
• D
• E

Q3:

The following graph is of the function , with its maximum at , minimum at , and zero at marked.

Find an expression for the inverse function when is restricted to the interval .

• A
• B
• C
• D
• E

What is the domain of in this case?

• A
• B
• C
• D
• E

Q4:

Consider the two following figures.

The first figure shows the graph of and a tangent to the graph with gradient 1. This tangent meets the graph at a point with -coordinate .

The second figure shows the graphs of and its inverse . The graphs cross in the third quadrant and touch in the first quadrant.

What is the value of ?

• A
• B
• C
• D
• E

What are the -coordinates of the two points of intersection of the graphs in the second figure?

• A and
• B and
• C and
• D and
• E and

Q5:

The graphs of and its inverse intersect at three points, one of which is .

Determine the value of .

• A
• B
• C
• D
• E

Find the -coordinate of the point marked on the figure.

• A
• B
• C
• D
• E

Find the -coordinate of the point marked on the figure.

• A
• B
• C
• D
• E

Q6:

The following graph is of the function , with its maximum at , minimum at , and zero at marked.

Find an expression for the inverse function when is restricted to the interval .

• A
• B
• C
• D
• E

What is the domain of in this case?

• A
• B
• C
• D
• E

Q7:

The following graph is of the function , with its maximum at , minimum at , and zero at labeled.

Find an expression for the inverse function when is restricted to the interval .

• A
• B
• C
• D
• E

What is the domain of in this case?

• A
• B
• C
• D
• E

Q8:

Determine whether the inverse of the represented function is a function or not.

• ANot a function
• BA function

Q9:

In the given figure, the green points represent the function . Do the blue points represent ?

• ANo
• BYes

Q10:

By sketching the graphs of and for , determine whether they are inverse functions.

• AThey are not inverse functions.
• BThey are inverse functions.

Q11:

By sketching the graphs of and for , determine whether they are inverse functions.

• AThey are not inverse functions.
• BThey are inverse functions.