3-1 Symmetry and Coordinate Graphs

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3-1 Symmetry and Coordinate Graphs

• Pre Calc A

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Point Symmetry

• Symmetric about the origin any point in Quadrant
  I has a point in Quadrant III (rotate 180)

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Determining Point Symmetry Algebraically

• A function, f(x) is symmetric about the origin if
  and only if f(-x) -f(x)

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Ex 17

• Determine whether each function is symmetric with
  respect to the origin.
• a. f(x) x6 b. g(x) -3x3 5x

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Line symmetry
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Determining Line Symmetry Algebraically

• For all f(x) when testing for line symmetry the
  equation must be equal to the original.

x-axis (a, -b)
y-axis (-a, b)
y -x (-b, -a)
y x (b, a)
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Ex

• Determine whether the graph of x² y 3 is
  symmetric with respect to the x-axis, y-axis, y
  x, and y -x

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Ex last one

• With a partner determine whether the graph of
  is symmetric to the origin, x-axis,
  y-axis, yx, and y -x.