# 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)

**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.