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3-2 Families of Graphs Pre Calc A

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Parent Graphs

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Changes to Graph Reflections Over x-axis: y = -f(x) Over y-axis: y = f(-x) Dilations Vertical: y = c f(x) c>1 stretch 0<c<1 Compression Horizontal: y = f(cx) c>1 compression 0<c<1 stretch Translations Up: y = f(x) + c Down: y = f(x) – c Left: y = f(x+ c) Right: y = f(x – c) Other Changes y = |f(x)| reflects any part of the parent graph that is below the x-axis, so that it is above the x -axis

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Ex 17: Use the parent graph y = x³ to sketch the graph of each function y = x³ - 1 y = (x – 1)³ y = (x – 1)³ + 3

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Ex : Graph the function and describe the movement f(x) = |(x + 1)² - 2| f(x) = (x + 1)² - 2

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