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1.7 Transformations of Functions Ex. 1 Shifting Points in the Plane 2 2 2 4 -2 Shift the triangle three units to the right and two units up. What are the three new ordered pairs? -

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Summary of Graphs of Common Functions f(x) = c y = x y = x 2 y = x 3

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Vertical and Horizontal Shifts On calculator, graph y = x 2 graph y = x 2 + 2 y = x 2 - 3 y = (x – 1) 2 y = (x + 2) 2 y = -x 2 y = -(x + 3) 2 -1

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Vertical and Horizontal Shifts 1.h(x) = f(x) + cVert. shift up 2.h(x) = f(x) - cVert. shift down 3.h(x) = f(x – c)Horiz. shift right 4.h(x) = f(x + c) Horiz. shift left 5.h(x) = -f(x) Reflection in the x-axis 6.h(x) = f(-x)Reflection in the y-axis

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Transformations on the Coordinate Plane. Example 2-2a A trapezoid has vertices W(–1, 4), X(4, 4), Y(4, 1) and Z(–3, 1). Trapezoid WXYZ is reflected.

Transformations on the Coordinate Plane. Example 2-2a A trapezoid has vertices W(–1, 4), X(4, 4), Y(4, 1) and Z(–3, 1). Trapezoid WXYZ is reflected.

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