Even And Odd Functions

An even function exists when f\left( x \right) =f\left( -x \right) for all values of x.

The graph of an even function must be symmetrical about the y-axis.

Examples of even functions have been listed below:

f\left( x \right) ={ x }^{ 2 }

f\left( x \right) ={ x }^{ 4 }

f\left( x \right) =cosx


An odd function exists when f\left( x \right) =-f\left( -x \right) for all values of x.

Graphs of odd functions should have 180 degrees rotational symmetry about the origin (0,0).

Examples of odd functions are listed below:

f\left( x \right) =x

f\left( x \right) ={ x }^{ 3 }

f\left( x \right) =sinx


Most functions are neither even or odd.

An example of a function that is neither even or odd would be:

f\left( x \right) ={ x }^{ 2 }+\frac { 1 }{ x }