or ODD EVEN Functions

TESTING FUNCTION FOR SYMMETRY

Test a function for symmetry with respect to the y-axis Substitute –x for x and see if you have equivalent functions

Symmetry equivalent to

SYMMETRIC WITH RESPECT TO the y-axis EVEN FUNCTION

NEXT

Test for symmetry of a function with respect to the origin Substitute –x for x and –f(x) for f(x) and see if you have equivalent functions

Symmetry equivalent to

SYMMETRIC WITH RESPECT TO THE ORIGIN ODD FUNCTION

Why don’t we talk about FUNCTIONS symmetric with respect to: x-axis NOT A FUNCTION

First Example

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither COMPARE ? EVEN YES

NEXT EXAMPLE

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither Simplify

Determine whether each function is even, odd, or neither COMPARE ? NO

Determine whether each function is even, odd, or neither COMPARE NOT EVEN ?

Now See If It's ODD

Determine whether each function is even, odd, or neither Start Here Need

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither COMPARE ? YES ODD

NEXT EXAMPLE

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither COMPARE ? NO

Determine whether each function is even, odd, or neither COMPARE NOT EVEN ?

Now See If It's ODD

Determine whether each function is even, odd, or neither Start Here Need

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither

Determine whether each function is even, odd, or neither COMPARE ? NO

Determine whether each function is even, odd, or neither COMPARE NOT ODD ?

Determine whether each function is even, odd, or neither COMPARE NOT EVEN NOT ODD ?

Determine whether each function is even, odd, or neither COMPARE ? Neither

SYMMETRIC WITH RESPECT TO the y-axis EVEN FUNCTION

SYMMETRIC WITH RESPECT TO THE ORIGIN ODD FUNCTION

NOT EVEN NOT ODD Neither

Graphic Examples

Even, Odd, Neither? ?

SYMMETRIC WITH RESPECT TO the y-axis Even, Odd, Neither? SYMMETRIC WITH RESPECT TO the y-axis

Even, Odd, Neither? EVEN

NEXT

Even, Odd, Neither? ?

SYMMETRIC WITH RESPECT TO THE ORIGIN

SYMMETRIC WITH RESPECT TO THE ORIGIN

Even, Odd, Neither? ODD

NEXT

Even, Odd, Neither? ?

Even, Odd, Neither? Neither