1. 1.6 Transformations of Parent Functions Part 2
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2. Learning Goal
understand the roles of a, d and c in function transformations f(x) is the parent function g(x) = af(x-d) +c

3. Vertical & Horizontal Translations
Vertical Translation graph moves up or down Horizontal Translation graph moves right or left

4. Reflection in the X-Axis

5. Vertical Stretches & Compressions

6. What You NEED to know how to quickly graph the parent functions
their tables of values
domain & range

7. Linear Function

8. Quadratic Function

9. Square Root Function

10. Reciprocal Function

11. Reciprocal Function

12. Absolute Value Function

13. Transformations of Parent Functions
y = af (x - d) + c
Describe the roles of the following: c d a

14. Vertical Translations y = af (x - d) + c
c > 0, graph is vertically translated c units up
c < 0, graph is vertically translated c units down

15. Vertical Translations

16. Vertical Translations

17. Horizontal Translations y = af (x - d)+ c
d > 0, graph is horizontally translated d units to the right
d < 0, graph is horizontally translated d units to the left

18. Horizontal Translations

19. Horizontal Translations

20. Vertical Stretches, Compression, Reflections y = af (x - d) + c
a < 0 (a is a negative number), graph is vertically reflected in the x-axis (line y = 0)

21. Vertical Stretches, Compression, Reflections y = af (x - d) + c
|a| > 1, graph is vertically stretched by a factor of |a|
|a| < 1 (or -1< a <1) , graph is vertically compressed by a factor of |a|

22. Vertical Reflections

23. Vertical Stretches

24. Vertical Compressions

25. EXAMPLE 1
Graph each pair of functions on the same grid. a) y = x2 y = -2(x + 1)2 – 3 b) y = √x y = -√x + 4 c) y = 1 y = 2_ x x-3 d) y = |x| y = ½|x+2|-1

26. EXAMPLE 2
The graph of y = x2 and a translation image are given. Write an equation for the translated function.

27. EXAMPLE 3
The graph of y = f (x) is given. On the same grid, graph y=f(x) + 4 and y = f(x) -3.

28. HomeFUN  pg 70-71 # 4ae, 5ac, 7a, 8a, 9a, 10abdf
Complete 1.7 Investigation – Stretches, Compressions & Reflections