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Transformations

Transformations - Transformations of functions 1 Objectives...

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1 Transformations of functions

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2 Objectives: 1. Given a function, describe the geometric transformations on that function. 2. Given a set of geometric transformations on a given function, rewrite the new function. 3. Sketch a graph using geometric transformations.
3 The independent variable of a function is also called the “argument” of the function. f(x) = (x-2) 2 + 3 the function the argument of the function

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4 Vertical Shifting Adding a constant to a function shifts its  graph vertically.
5 -4 -3 -2 -1 1 2 3 4 -3 -2 -1 1 2 3 3 2 3 2 3 2

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6 Vertical Shifts y = f(x) + c (c > 0), shifts the graph of f(x) up  “c” units  y = f(x) - c (c > 0), shifts the graph of f(x)  down “c” units
7 Horizontal Shifting Adding a constant to an argument of a   function shifts its graph horizontally.

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8 -4 -3 -2 -1 1 2 3 4 -3 -2 -1 1 2 3 y = x 3 3 y = (x + 3) 3
9 Horizontal Shifts y = f(x – c) (c > 0), shifts the graph of y = f(x) to the right “c” units y = f(x + c) (c > 0), shifts the graph of y = f(x) to the left “c” units

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