Graphing Techniques Lesson 2.7

2 What Do the Constants Do?  Given  What affect do the constants have on the graph when we change them? a  Amplitude, height above/below base value b  Period length, how long till repeats itself c  Phase shift, graph shifted right or left d  Shift Whole curve up or down Experiment with the Spreadsheet and make conclusions Spreadsheet Experiment with the Spreadsheet and make conclusions Spreadsheet View Web Demo

3 Amplitude  The absolute value |a| is the amplitude

4 Period  Period for sin, cos, sec, csc =

5 Phase Shift  Phase shift for sin, cos, sec, csc =

6 Vertical Shift  Vertical shift = d

7 Combining the Transformations  If you know this is a graph of the sin function, can you determine the values for a, b, c, and d? A-2 B0.5 C D

8 Try It Out  Determine the amplitude, phase shift, and period for the following

9 Addition of Ordinates  We can add two functions by adding the y values for a given x y = x + sin x y = x y = sin x y = x + sin x

10 Add Those Ordinates  Try these Graph the functions separately Then the combination

11 Assignment A  Lesson 2.7A  Page 199  Exercises 1 – 61 EOO

12 Assignment B  Lesson 2.7B  Page 200  Exercises 61 – 79 odd