Odd or Even functions

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Basic functions and transformations/graphing polynomials and rational functions

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Transformations, Symmetries, and Tilings

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Sinusoidal and Periodic Functions

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Final Exam - MCR 3U

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Transformations

Rigid transformations

Reflections

Reflection in the y-axis: h(x) = f(-x)

Reflection in the x-axis: h(x) = -f(x)

Reflection on x-axis

Vertical and Horizontal shifts c= posotive real number

Horizontal shift c units to the left: h(x) = F(x+c)

Horizontal shift

Horizontal shift c units to the right: h(x) = F(x-c)

Vertical shift c untis downward: h(x) = f(x) - c

Vertical Shift

Vertical shift c units upward: h(x) = f(x) + c

Nonrigid transformations on Y = f(x) looks like

g(x) = cf(x)

Vertical shrink if 0 < c < 1

Vertical stretch if c > 1

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