1. Section 1-7 TRANSFORMATIONS OF FUNCTIONS

2. What do you expect? a)f(x) = (x – 1) 2 + 2 Right 1, up 2

3. b) f(x) = - | x + 3 | reflected over the x-axis, left 3

4. Let’s focus on the left/right shifts and really understand why it is opposite the sign. c)f(x) = (x – 5) 2 We anticipate a horizontal shift right 5. But why is it minus/move right? Let f(x) = 0 and solve for x. What are you really finding when you let f(x) = 0? 0 = (x – 5) 2 0 = x – 5 5 = x (5, 0) is the x-intercept

5. F(x) = -(x – 4) 2 What do you anticipate?

6. What happens when I make this subtle change? f(x) = (-x – 4) 2 Set f(x) = 0 and solve and believe. So, where does the (-) have to be for the graph to reflect over the x- axis?

8. Look at the difference between the position of the (-) and the change in the graphs

9. See if you can transfer these same ideas to cubic functions. F(x) = x 3 +5F(x) = -x 3 – 2

10. Look at absolute value in the same way F(x) = |-x|F(x) = -|x| Reflected over y-axis Reflected over x-axis

11. Non-Rigid Transformations (stretching/shrinking) Vertical Stretch Vertical Shrink

12. Non-Rigid Transformations (stretching/shrinking) Horizontal Shrink Horizontal Stretch

13. When the change is made… Outside the function the transformation is a vertical change A value > 1 means stretch A value greater than 0 but less than 1 means shrink Inside the function, the transformation is a horizontal change A value > 1 means shrink A value greater than 0 but less than 1 means stretch