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Unit 1: Functions Minds On More Graphing!!!

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Unit 1: Functions Minds On Graph the following functions: f(x) = x 2 g(x) = 3f(x) h(x) = -g(x)

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Learning Goals: I can vertically stretch and compress a function. I can horizontally stretch and compress a function. I can transform a function using translations, reflections, and stretches and compressions.

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together How does the value “a” in the function y = af(x) change the graph of f(x)? When a > 1 f(x) is stretched vertically by a factor of a When 0 < a < 1, f(x) is compressed vertically by a factor a AND When a is negative, f(x) is ALSO reflected in the x-axis.

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Let’s look at y = f(kx) WARNING! This “k” is not the same as k in y = a(x-h) 2 + k

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together f(x) = x 2 g(x) = f(3x) h(x) = 3f(x) Are g(x) and h(x) the same?

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Graph the following functions: f(x) = x 2 g(x) = f(3x) h(x) = 3f(x)

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together How does the value “k” in the function y = f(kx) change the graph of f(x)?

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together We need to apply transformations in a specific order: 1.Reflections, Stretches and/or compressions in any order 2.Translations

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together List the transformations that would be applied to f(x) to get g(x): g(x) = -2f(3x – 12) - 5

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together If f(x) = x 2, determine the corresponding equation for g(x): g(x) = -2f(3x – 12) – 5

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformations

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Given the graph of f(x), graph the indicated transformation

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Sketch the graph of g(x)

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Unit 1: Functions Lesson 7: Stretches, Compressions, and Putting it all Together Homework Page 102#12 Page 120#4ce Page 129 #1, 2, 3, 4, 7

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