Even and Odd Functions
More Lessons for PreCalculus
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.
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