Question

How do you determine if `y=x³+x-3` is an even or odd function?

Answer 1

neither odd/even

Explanation:

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

• 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)^3 + (-x) - 3 = -x^3 - x - 3 ≠ f(x) " Not even "`

Test for odd :

`-f(x) = -(x^3+x-3) = -x^3-x+3 ≠ f(-x)" Not odd "`

Hence function is neither even nor odd.