Even and Odd Funtions

Even Functions

The equation, f(-x)=f(x), is used to define an even function.


For every input, (x) or (-x), the output (y) will always be the same.

• The x can be either negative or positive but the y will come out the same.
  

This results in the graph being symmetrical about the y-axis.

• A graph in Quadrant 1 would be reflected onto Quadrant 2, as if it was flipped by a mirror. (Also, can work for Quadrant 3 and 4.)

Example:

The graph above is x^2.

If 2 was plugged in, (x) , then the result will be 4, (y).

If -2 was plugged in, (-x), then the result will still be 4, (y).

Odd Functions

The equation, f(-x)=-f(x) , can be used to define an odd function.

The graph will be symmetrical about the origin.

• A graph in Quadrant 1 would be reflected onto Quadrant 3, as if it was flipped diagonally. (Also, can work for Quadrant 2 and 4.)
  

Example:

The graph above is x^3.

If 2 was plugged in, (x), then the result will be 8, (y).

If -2 was plugged in, (-x), then the result would be -8, (-y).

If (x,y) exists on the graph, then point ( -x, -y) also has to exist.

• This goes for the same for (-x,y) and (x, -y).