3-1 Symmetry and Coordinate Graphs. Graphs with Symmetry.

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3.1 Symmetry & Coordinate Graphs

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Presentation transcript:

3-1 Symmetry and Coordinate Graphs

Graphs with Symmetry

Symmetry with Respect to the Origin Symmetric with the origin if and only if the following statement is true: F(-x)=-F(x)

Are the following Symmetric with Origin? 1)F(X) = x 5 2)F(x) = x/(1-x) 3) F(x) = 7x 2 + 3x + 1

Graphs can also be symmetric around certain lines. They can be symmetric around the x-axis, y-axis, y=x, or y=-x.

X-axis : To test, plug in (x,-y) Y-axis To test, plug in (-x,y)

Y=x To test, plug in (y,x) Y= -x To test, plug in (-y,-x)

3) Determine whether the graph of xy=-2 is symmetric with respect to the x axis, y axis, the line y=x, and the line y=-x, or none of these?

Determine whether the graph of │ y │ = │ x │ +1 is symmetric with respect to the x axis, yaxis, both or neither?

Even and Odd Functions Even Functions: Symmetric with respect to Y axis Odd Functions  Symmetric with respect to the origin

Even and Odd Functions Which lines are lines of symmetry for the graph of x 2 =1/y 2. Is it even, odd, or neither? Is the following function symmetric about the origin? Is it even or odd? F(X)=-7x 5 + 8x

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