### Home > APCALC > Chapter 1 > Lesson 1.2.2 > Problem 1-43

Copy the graph at right. Then complete it so it will have each type of symmetry described below.

Reflection symmetry across the

-axis.Reflection symmetry across the

-axis.Point symmetry about the origin. (This means a

rotation about the origin leaves the graph unchanged.) Recall the definitions of even and odd functions. For each part above, state if the graph is even, odd, or neither.

**Even and Odd Functions**

A function *f* is an **even function **if, for all *x* in its domain, *f*(–*x*) = *f*(*x*).

A function *f* is an **odd function **if, for all *x* in its domain, *f*(–*x*) = –*f*(*x*).

Example: If *f*(*x*) = 2*x*^{3} + sin(*x*), then *f*(–*x*) = 2(–*x*)^{3} + sin(–*x*)

= 2(–1)^{3}*x*^{3} + (–1)sin(*x*)

= –2*x*^{3} – sin(*x*) = –(2*x*^{3} + sin(*x*))

Therefore *f*(–*x*) = –*f*(*x*), so *f* is odd.

Use the eTool below to view the graphs.

Click the link at right for the full version of the eTool: *Calc 1-43 HW eTool*