Even and Odd Functions Worksheet

Solutions

Determine if the following functions are even or odd:

1 f(x) = x6 + x 4 - x 2

2f(x) = x5+ x3 - x

3 f(x)= x |x|

4f(x) = |x| − 1

5 Even Function

6 Odd Function


1

Determine if the function is even or odd.

f(x) = x6 + x4 − x 2

f(x)= (x)6 + (x)4 − (x) 2 = x 6 + x 4 − x 2 = f(x)

The function is even and symmetrical about the vertical axis.


2

Determine if the function is even or odd.

f(x) = x5 + x3 − x

f(x)= (−x)5 + (−x) 3 − (−x) = −x5 − x 3 + x = −f(x)

The function is odd and symmetrical about the origin.


3

Determine if the function is even or odd.

3 f(x)= x |x|

f(−x) = −x |−x|= −x |x|= −f(x)

The function is odd and symmetrical about the origin.


4

Determine if the function is even or odd.

4f(x) = |x| − 1

f(−x) = |−x| − 1= |x| − 1 = f(x)

The function is even and symmetrical about the vertical axis.


5

Determine if functions are even or odd:

1 Even Function

Function Operations

The function is even and symmetrical about the vertical axis.


6

Determine if the function is even or odd.

2 Odd Function

Function Operations

The function is odd and symmetrical about the origin.