3-1 symmetry and coordinate graphs. graphs with symmetry
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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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