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

  1. Reflection symmetry across the -axis.

  2. Reflection symmetry across the -axis.

  3. Point symmetry about the origin. (This means a rotation about the origin leaves the graph unchanged.)

  4. Recall the definitions of even and odd functions. For each part above, state if the graph is even, odd, or neither.

Increasing curve, starting at the origin, opening down, passing through the points (1, comma 1), & (4, comma 2).

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) = 2x3 + sin(x), then f(–x) = 2(–x)3 + sin(–x)

                               = 2(–1)3x3 + (–1)sin(x)

                               = –2x3 – sin(x) = –(2x3 + 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