Question

How do you determine if `f(x)= x^5` is an even or odd function?

Answer 1

f(x) is an odd function.

Explanation:

To determine if f(x) is even/odd consider the following.

• If f(x)= f( -x) , then f(x) is even`AAx" in the domain"`

Even functions have symmetry about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd `AAx" in the domain"`

Odd functions have half-turn symmetry about the origin.

Test for even

`f(-x)=(-x)^5=-x^5≠f(x)" hence not even"`

Test for odd

`-f(x)=-x^5=f(-x)" hence f(x) is an odd function"`
graph{x^5 [-10, 10, -5, 5]}