# Even and Odd Functions

Related Topics:
More Lessons for PreCalculus

Math Worksheets

Videos, worksheets, solutions, and activities to help PreCalculus students learn about even and odd functions.

Symmetry of Graphs: Odd and Even Functions :
There are special types of functions that have graph symmetry. The most notable types are even and odd functions. Even functions have graph symmetry across the y-axis, and if they are reflected, will give us the same function. Odd functions have 180° rotational graph symmetry, if they are rotated 180° about the origin we will get the same function. There are also algebraic ways to compute if a function is even or odd which are shown below.
How can you tell if a function is even?
Four ways to find out if a function is even.
1. y-axis (vertical) symmetry
2. all even exponents
3. if (a, b) is on the line, so is (-a, b)
4. f(x) = f(-x)
How can you tell if a function is odd?
Find out four ways to test if a function is odd.
1. origin (rotational) symmetry
2. all odd exponents
3. if (a, b) is on the line, so is (-a, -b)
4. f(-x) = -f(x)

Is the function even, odd, or neither? Use the graph to decide.
In this video, we look at the graph to determine if a given function is even, odd, or neither.
Even and odd functions
Discuss algebraic and geometric properties of even and odd functions.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.