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

For each function sketched below, sketch and compare it with the original graph. Then describe its symmetry.

a.

What does mean?

Compare

*and*

Compare

*and*

keep going...

*and*

The sketch of should be identical to the given graph

*.*

b.

On this graph, .

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

*-values in the negative region.*

c. EVEN AND ODD FUNCTIONS—INFORMALLY

A function that is symmetric with respect to the *y*-axis, like the one in part (a) above, is called an **even function**. A function that is symmetric with respect to the origin, like the one 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 that you have studied in a previous course, 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.*