### Home > CALC > Chapter 1 > Lesson 1.1.1 > Problem 1-10

For each function sketched below, sketch

*and compare it with*

*. Then describe its symmetry.*

What does

mean?

Compareand

Compareand

keep going...andThe sketch of

should be identical to the given graph.

On this graph,

.Plot all negative

-values in the positive region, and plot all positive-values in the negative region.

EVEN AND ODD FUNCTIONS--INFORMALLY

A function that is symmetric with respect to the-axis, like that in part (a) above, is called an**even**function. A function that is symmetric with respect to the origin, such as that in part (b), is called an**odd**function.

Sketch examples of even and odd functions. Include how you can test whether a function is even or odd. Then list some famous even/odd functions from your parent graphs, and the symmetries associated with even and odd functions.

Even functions are symmetrical ACROSS the -axis, they have reflective symmetry. Odd functions are symmetrical ABOUT the origin, they have

Graph (a) is even. Graph (b) is odd.

Famous even functions include: ,

*,*

*, and all vertical translations and stretches of the graphs above.*

Famous odd functions include: ,

*,*

*, and all stretches of the graphs above.*