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

2. Graph the following functions:
Unit 1: Functions
Minds On
Graph the following functions:
f(x) = x2
g(x) = 3f(x)
h(x) = -g(x)

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

7. Lesson 7: Stretches, Compressions, and Putting it all Together
Unit 1: Functions
Lesson 7: Stretches, Compressions, and Putting it all Together
Graph the following functions:
f(x) = x2
g(x) = f(3x)
h(x) = 3f(x)

8. Lesson 7: Stretches, Compressions, and Putting it all Together
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)?
When k > 1 or k < -1 f(x) is compressed horizontally by a factor of 1 𝑘
When -1 < k < 1, f(x) is stretched horizontally by a factor of 1 𝑘
AND
When k is negative, f(x) is ALSO reflected in the y-axis.

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

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

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

12. Lesson 7: Stretches, Compressions, and Putting it all Together
Unit 1: Functions
Lesson 7: Stretches, Compressions, and Putting it all Together
Graph the following function:
f(x) = - 2(𝑥+1) −3

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

14. Lesson 7: Stretches, Compressions, and Putting it all Together
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. Lesson 7: Stretches, Compressions, and Putting it all Together
Unit 1: Functions
Lesson 7: Stretches, Compressions, and Putting it all Together
If f(x) = x2, determine the corresponding equation for g(x): g(x) = -2f(3x – 12) – 5

16. Lesson 7: Stretches, Compressions, and Putting it all Together
Unit 1: Functions
Lesson 7: Stretches, Compressions, and Putting it all Together
If f(x) = 𝑥 , determine the corresponding equation for g(x): 𝑔(𝑥) = 3𝑓(−2𝑥 + 8) − 1

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

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

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

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

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

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

23. Lesson 7: Stretches, Compressions, and Putting it all Together
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