Review - Functions and Inverses Name ______

Math 2 with Support

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.c. Explore the graphs of functions and their inverses.

Graph the following functions. DO NOT graph the inverse. Determine the domain and range of the function and the inverse and tell whether they are functions.

1.

Inverse

D: D:

R: R:

Function (Yes/No) Function (Yes/No)

One-to-One?

2.

Inverse

D: D:

R: R:

Function (Yes/No) Function (Yes/No)

One-to-One?

3. Create a t-chart for the function and its inverse. Graph each. Find the domain and range for each.

Inverse Function

x / y
x / y

Domain:

Range:

Inverse

Domain:

Range:

4. What line is a function and its inverse reflected over?

MM2A5.b Determine inverses of linear, quadratic, and power functions and functions of the form f(x)=a/x.

Find the inverses of the following functions:

1. 2.

3. 4.

5. 6.

MM2A5.d. Use composition to verify that functions are inverses of each other.

1. What do composition of functions need to equal in order for the functions to be inverses of each other?

Determine if f(x) and g(x) are inverses of each other by using composition.

2.

3.

4.

5. Which of the following pairs of functions are NOT inverses of each other?

a. b.

c. d.

Answer Key:

1. The graph is a line.
X / y
-2 / 11
-1 / 7
0 / 3
1 / -1
2 / -5
Domain:
Range:
It is a function.
Inverse:
Domain:
Range:
It is a function.
It is one-to-one.
2. The graph is a quadratic equation with vertex (-2, -5).
x / y
-4 / -1
-3 / -4
-2 / -5
-1 / -4
0 / -1
Domain:
Range:
It is a function.
Inverse:
Domain:
Range:
It is NOT a function.
It is NOT one-to-one.
3.
x / y
-2 / 7
-1 / -2
0 / -5
1 / -2
2 / 7
Function
Domain:
Range: / 3 continued:
Inverse:
x / y
7 / -2
-2 / -1
-5 / 0
-2 / 1
7 / 2
Domain:
Range:
4. y=x
------
1.
x = -3y + 5
-5 -5
x-5= -3y
-3 -3

2.


yx = 5
y y

3.



-4 -4
- 4 =
4.

+7 +7

/ 5.

+5 +5



6.



-1 -1

------
1. x
2.
= x + 4 – 4
= x

=
= x
They are inverses.
3.
= x + 3 + 3
= x +6

=
= x – 1
They are not inverses.
4.
= x – 3 + 3
= x / 4 continued:

=
= x
5. B