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Even and Odd Identities

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

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Even and Odd Functions

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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.

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