Question

How do you determine if `x^3-5` is an even or odd function?

Answer 1

neither

Explanation:

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

• If the function is even then f(x) = f(-x), for all x

Even functions have symmetry about the y-axis

• If the function is odd then f(-x) = - f(x), for all x

Odd functions have symmetry about the origin

Test for even :

f(-x) `= (-x)^3 - 5 = - x^3 - 5 ≠` f(x) hence not even

Test for odd :

`- f(x) = - (x^3 - 5) = - x^3 + 5 ≠ f (- x)" hence not odd "`

The function `x^3 - 5 " is neither even nor odd "`