# 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

6

## 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

The function is even and symmetrical about the vertical axis.

## 6

Determine if the function is even or odd.

2

The function is odd and symmetrical about the origin.