What do The Graphs of Even and Odd Functions look like?

Even Functions

Algebraically, an even function is one that conforms to the following rule:

$$f(-x) = f(x)$$

In English, this means that even if you make a certain input negative, the output will not change. Both $3$ and $-3$ will result in the same output value. What does that look like on a graph?

Even functions, when graphed, have symmetry with the $y$-axis.

Odd Functions

Algebraically, an odd function is one that conforms to the following rule:

$$f(-x) = -f(x)$$

In English, this means that if you make a certain input negative, the output will also change signs. For example, if our function is odd, we would input $3$ and get $5$ and input $-3$ and get $-5$. What does that look like on a graph?

Odd functions, when graphed, have symmetry with the origin.