Practice Even and Odd Functions in Math

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

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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.

Showing a random 20 of 50 problems.

Example 1

medium
Classify f(x)=x3−x.

Example 2

easy
Is f(x)=x2+2x+1 even, odd, or neither?

Example 3

medium
Classify f(x)=cos⁡(x).

Example 4

medium
Classify f(x)=sin⁡(x).

Example 5

challenge
Given f(x)=x3+2x2+x+5, decompose it into even part E(x) and odd part O(x).

Example 6

challenge
Show that any function f can be written as a sum of an even and an odd function.

Example 7

hard
Classify f(x)=x2sin⁡(x).

Example 8

easy
Is f(x)=x2 even, odd, or neither?

Example 9

challenge
If f is even and g is odd, classify the composition f∘g (i.e., f(g(x))).

Example 10

easy
Is f(x)=−x even, odd, or neither?

Example 11

easy
Is f(x)=x6 even, odd, or neither?

Example 12

medium
If f is odd and f(3)=7, find f(−3).

Example 13

medium
If f is even and g is even, classify the product f⋅g.

Example 14

easy
Classify f(x)=tan⁡(x).

Example 15

medium
If f is even and f(−2)=9, find f(2).

Example 16

easy
Is f(x)=5 even, odd, or neither?

Example 17

medium
If f is even, what does its graph have? (Pick one: y-axis symmetry / origin symmetry.)

Example 18

easy
Is f(x)=4x3−x even, odd, or neither?

Example 19

easy
Is f(x)=∣x∣ even, odd, or neither?

Example 20

easy
Is f(x)=x5 even, odd, or neither?
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