1. Section 3.1.3 Equivalent Transformations

2. Lesson Objective: Students will: Understand that a vertical stretch of y = x² is equivalent to a horizontal stretch by a different factor. Understand that a vertical stretch of is equivalent to a horizontal shift.

3. Recall: In Lesson 3.1.1, you investigated and compared horizontal and vertical stretches. You can now shift and stretch graphs both horizontally and vertically. In this lesson you will see how two different transformations of exponential functions can be equivalent.

4. Now consider: Writing a function of the form then transforming it to an equivalent function of the form

5. 3-31: a: compressed horizontally by 2. b: a = 4 c: It is stretched vertically by 4. d: Yes, they have the same equation If you can’t fill in the following blanks, you should review exponent laws now!! = _____. _____.

6. 3-32: a: It is stretched vertically by a factor of 3. b: See graph below. c: (0, 3)

7. 3-33: a: A vertical stretch times 3 and a shift up 1. b: See graph below. c: y = 1 d: (0, 4) e: (0, A + B)

8. 3-34:

9. 3-35: a: is shifted left 2 units and stretched vertically by 3. b: (0, 12) c: d: Yes, because

10. 3-36: a: b:

11. Closure 1.Given, what is the value of a in that will generate the same graph as f (x)?

12. Closure 2. Find A so that is equivalent to 3. Find h so that is equivalent to

13. Closure 4. Find h so that is equivalent to

14. Assignment Pg 134 #3-39 TO 3-49