1. Today in Pre-Calculus Do NOT need a calculator Go over homework
Notes: Non-Rigid Graphical Transformations
Homework

2. Homework 2) up 5.2 4) Right 3 6) Down 100 8)Left 50 down 279
18)Reflect over x-axis, left 4
30)

3. Non-Rigid Transformations
Changes the size and shape of the graph.
Types:
Stretches
Shrinks
Can be vertical or horizontal

4. Vertical Multiply equation by a factor c: y = c∙f(x)
If c > 1, stretch by a factor of c
If c < 1, shrink by a factor of c
y=x3-5x
y=2(x3-5x)
y=1/2(x3-5x)

5. Horizontal Divide the x in the function by c:
If c > 1, stretch by a factor of c
If c < 1, shrink by a factor of c
y=x3-5x
y=(x/3)3-5(x/3)
y=(x/.5)3-5(x/.5)

6. Misc
Reflections: If c is negative in either the vertical or horizontal stretch/shrink, the graph reflects and stretches/shrinks.
Order matters when combining transformations
Stretch/shrink
Reflections
Shifts

7. Example Basic function: x2 Key points: (0,0), (1,1), (-1,1)
Vertical stretch 3 (multiply y by 3)
Down 4

8. Example Basic function: x3 Key points: (0,0), (1,1), (-1,-1)
Reflect over x-axis
Vertical stretch 1/2 (multiply y by 1/2)
Right 3

9. Example
b. y = 0.5f(x + 1) – c.
y = f(x – 2) + 3

10. Homework
Pg 147: 13-16, 21, 24, 26, 39, 43, 44, 47, 49, 51-54(use handout)
Memorize 10 basic functions
Quiz Monday, September 29