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3-1 Symmetry and Coordinate Graphs

3-1 Symmetry and Coordinate Graphs. Pre Calc A. Point Symmetry. Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate 180 ˚). Determining Point Symmetry Algebraically. A function, f(x) is symmetric about the origin if and only if f(-x) = -f(x). Ex 17:.

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3-1 Symmetry and Coordinate Graphs

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  1. 3-1 Symmetry and Coordinate Graphs Pre Calc A

  2. Point Symmetry • Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate 180˚)

  3. Determining Point Symmetry Algebraically A function, f(x) is symmetric about the origin if and only if f(-x) = -f(x)

  4. Ex 17: • Determine whether each function is symmetric with respect to the origin. a. f(x) = x6 b.g(x)= -3x3 + 5x

  5. Line symmetry

  6. 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)

  7. Ex : Determine whether the graph of x² + y = 3 is symmetric with respect to the x-axis, y-axis, y = x, and y = -x

  8. Ex last one: With a partner determine whether the graph of is symmetric to the origin, x-axis, y-axis, y=x, and y = -x.

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