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˚)

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y

x

y

Determining Point Symmetry Algebraically

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

Ex 17:

Determine whether each function is symmetric with respect to the origin.

a. f(x) = x6 b. g(x)= -3x3 + 5x

Line symmetry

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y

x

y

x

y

x

y

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)

Ex :

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

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.

xy

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