<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Even and Odd Identities

## Functions symmetric with respect to the y-axis or about the origin.

Estimated6 minsto complete
%
Progress
Practice Even and Odd Identities

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated6 minsto complete
%
Even and Odd Functions

Feel free to modify and personalize this study guide by clicking "Customize".

.

An even function is a function with a graph that is symmetric with respect to the 'y' axis and has the property that f(-x) = f(x)

An example of an even function would be a parabola like \begin{align*}y=x^2\end{align*} . Why would it be even using the definition above? Click here for guidence

An odd function is a function with the property that f(-x) = -f(x)

\begin{align*}y=x^3\end{align*} is an example of an odd function but what makes it an odd function? What can you infer using the definition above?

You can also involve trigonometric function to see if they are even or odd.

\begin{align*}\cos(-30^\circ) & = \cos 330^\circ = \frac{\sqrt{3}}{2} = \cos 30^\circ \\ \cos (-135^\circ) & = \cos 225^\circ = - \frac{\sqrt{2}}{2} = \cos 135^\circ\end{align*}

Tip: This depend on the degrees/radians of the function because it depicts the value of the equation which can change weather or not it is an even or odd function. Also, take in consideration the reference angle/coterminal angle of the negative angle to help you find the right values.

### Explore More

Sign in to explore more, including practice questions and solutions for Even and Odd Identities.