Question

How do you determine if `f (x) = (x)^2 -x` is an even or odd function?

Answer 1

neither odd nor even.

Explanation:

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

• If f(x) = f( -x) , then f(x) is even

Even functions have symmetry about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd

Odd functions have symmetry about the origin.

Test for even

`f(-x)=(-x)^2-(-x)=x^2+x≠f(x)`

Since f(x) ≠ f( -x) , then f(x) is not even.

Test for odd

`-f(x)=-(x^2-x)=-x^2+x≠f(-x)`

Since f( -x) ≠ - f(x) , then f(x) is not odd.

Thus f(x) is neither odd nor even.
graph{x^2-x [-20, 20, -10, 10]}