EVEN and ODD functions

Even Functions: An even function is when the function is symmetric about the y-axis.

The right side is mirror image of left hand side and the left side is mirror image of right hand side.

Mathematically speaking, if you plug in a (-x) in the place of a (x) you will get the same output.

For example: f(x) =7x² + 10

So I'll plug –x in for x, and simplify:

f(–x) =7(–x)² + 10
= 7(x²) + 10

= 7x² +10

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Odd Functions: An odd function is when a function is turned about, on it's origin, 180 degrees.



For example: f(x) = 6x³ – 3x

so I'll plug –x in for x, and simplify:

f(–x) = 6(–x)³ – 3(–x)
= 6(–x³) + 3x
= –6x³ + 3x

<To make it easy for me, I think of multiplying through the function by -1 >


This picture is a perfect example of what the 180 degrees turn on the origin looks like.