1. Transforming Graphs of Cosine Functions Mr
Transforming Graphs of Cosine Functions Mr. Peter Richard says: Don’t Cosine any Loans!

2. OBJECTIVES
1. Identify horizontal and vertical translations in the graph of sine function.
2. Graph the sine function with various phase shift and vertical shift.
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

3. d: is the Vertical Shift
Graphing
y = a cosine b(x – c ) + d
(x – c ): is the Horizontal Shift
d: is the Vertical Shift
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

4. Notes Over 6.4 Amplitude Period Translation left p
Graphing a Horizontal Translation
Graph the function.
Amplitude
Period
Translation
left p
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

5. Phase Shift = to the right, since c > 0
Examples: Graph
Amplitude =  3  = 3
Period =
Phase Shift = to the right, since c > 0
- 3 3
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

6. Notes Over 6.4 Amplitude Translation down 2 Period
Graphing a Vertical Translation
Graph the function.
Amplitude
Translation
down 2
Period
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

7. Vertical Translation = 3 units upward, since d > 0
Examples: Graph
Amplitude =  - 2  = 2
Period =
Vertical Translation = 3 units upward, since d > 0
- 2 2
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

8. Translate the Cosines! Quiz: Page 760/761 # 16, 18, 20, 26, 34
Homework: # 15, 17, 21, 31, 39
Copyright © by Houghton Mifflin Company, Inc. All rights reserved.