Question

Is the function `h(x) = x^3-5` even, odd or neither?

Answer 1

neither

Explanation:

To determine if a function is even/odd consider the following.

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

Even functions are symmetrical about the y-axis.

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

Odd functions are symmetrical about the origin.

Test for even

`f(-x)=(-x)^3-5=-x^3-5≠f(x)`

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

Test for odd

`-f(x)=-(x^3-5)=-x^3+5≠f(-x)`

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

hence f(x) is neither even nor odd.
graph{x^3-5 [-20, 20, -10, 10]}