1. Algebra 2 1-8 Exploring Transformations Stretch and Shrink

2. Big Idea We are going to explore graphs that expand by stretching or shrinking in a given direction. The general form equation we will explore is

3. Quick Questions How will “h” affect the function? How will “k” affect the function? Positives and negatives?

4. Example

8. Concept Summary

9. Mirror f(x) = af(x) When y is replaced with y/a, the function is stretched/shrunk in the vertical direction If a > 1 it is a vertical stretch if 0 < a < 1 it is a vertical shrink

10. Mirror f(x) = f(x/b) When x is replaced with x/b, the function is stretched/shrunk in the horizontal direction If b > 1 it is a horizontal stretch if 0 < b < 1 it is a horizontal shrink

11. Vocabulary Rigid Transformations – Transformations that produce an image that is congruent to the original Non-Rigid Transformations – Transformations that do not necessarily produce an image that is congruent to the original

12. Quick Questions What kind of transformation is a stretch, a shrink? What kind of transformation is a translation? What kind of transformation is a reflection?

13. Vocabulary Scale Factor – The amount of stretch or shrink applied to a transformation

14. Think Deep What would it take for a stretch or shrink to actually be rigid? Can you stretch in such a way, the result is the same? What if the stretch is with a factor of one? What if the stretch is with a scale factor of negative one?

15. Example

18. Practice

21. Horizontal Stretch of 3 Horizontal Shrink of 3 Reflected over the y-axis Vertical Stretch of 2 Reflected over the x-axis Vertical Shrink of 2

22. Practice Shifted up 2 Stretched in vertical direction by 3 Shifted left 7 Stretched in horizontal direction by 4

23. Shifted up 2 Stretched in vertical direction by 3 Shifted left 7 Stretched in horizontal direction by 4

24. Practice

25. Homework Pages 63 – 65 8 – 10, 25 – 27, 39 – 43