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Unit 1: Functions Minds On More Graphing!!!. 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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Presentation on theme: "Unit 1: Functions Minds On More Graphing!!!. Unit 1: Functions Minds On Graph the following functions: f(x) = x 2 g(x) = 3f(x) h(x) = -g(x)"— Presentation transcript:

1 Unit 1: Functions Minds On More Graphing!!!

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

3 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.

4 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.

5 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

6 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?

7 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)

8 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)?

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

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

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

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

13 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

14 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

15 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

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

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

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

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

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

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

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

23 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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