Practice Even and Odd Functions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Even means mirror across y-axis; odd means rotational symmetry through the origin.

Example 1

easy
Determine whether f(x) = x^4 - 3x^2 + 2 is even, odd, or neither.

Example 2

medium
Determine whether g(x) = \frac{x}{x^2 + 1} is even, odd, or neither.

Example 3

medium
Is h(x) = x^3 + x^2 even, odd, or neither?

Example 4

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