Even and Odd Functions Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Determine whether

f(x) = x^4 - 3x^2 + 2

is even, odd, or neither.

Answer

\text{Even}

A function is even if

f(-x) = f(x)

for all

x

in its domain, meaning its graph is symmetric about the

y

-axis. Polynomials with only even powers of

x

(including constant terms, which are

x^0

) are always even functions.

About Even and Odd Functions

An even function satisfies $f(-x) = f(x)$ (symmetric about $y$ -axis); an odd function satisfies $f(-x) = -f(x)$ (rotational symmetry about origin).

Determine whether [formula] is even, odd, or neither.

Is [formula] even, odd, or neither?

Prove that the product of two odd functions is an even function.