warm-up. functionsfunctions symmetric about the y axis symmetric about the origin

Warm-Up

Given , evaluate the following:

1.

2.

3.

4.

5.

FUNCTIONSSymmetric about the y axis

Symmetric about the origin

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8

7

123456

8

-2-3-4-5-6-7

For an even function: for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Even functions have y-axis Symmetry

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8

7

123456

8

-2-3-4-5-6-7

For an odd function: for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

Odd functions have origin Symmetry

2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8

7

123456

8

-2-3-4-5-6-7

We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function.

x-axis Symmetry

Even, Odd or Neither?Graphically

f x x x( ) 3Even, Odd or Neither?

Graphically

Even, Odd or Neither?Graphically

Even, Odd or Neither?Graphically

Given

A function is even if for every number x in the domain.

If you plug a –x into the function and you get the original function back again, the function is even.

Same!Even Function

Given

A function is odd if for every number x in the domain.

If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function

is odd.

Odd Function

ALL signs of the terms changed!

A function is even if for every number x in the domain.

If you plug a –x into the function and you get the original function back again, the function is even.

125 24 xxxf Is this function even?

1251)(2)(5 2424 xxxxxfYES

xxxf 32 Is this function even?

xxxxxf 33 2)()(2NO

A function is odd if for every number x in the domain.

If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function

is odd.

125 24 xxxf Is this function odd?

1251)(2)(5 2424 xxxxxfNO

xxxf 32 Is this function odd?

xxxxxf 33 2)()(2YES

Odd, Even, or Neither?

Even Function

Odd, Even, or Neither?

Neither Odd or Even

Odd, Even, or Neither?

Odd Function