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) = x5

2)F(x) = x/(1-x)

3) F(x) = 7x2 + 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 x2=1/y2. Is it even, odd, or neither?

• Is the following function symmetric about the origin? Is it even or odd?• F(X)=-7x5 + 8x

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