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 of the point marked on the figure.
- A
- B
- C
- D
- E
Find the 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.