1. 9.2/9.3 Transformation
Brett Solberg AHS ‘11-’12

2. Warm-up Test for all three types of symmetry 1) 2x4 + 3 = y2
Are the following functions even or odd?
3) f(x) = |3x|
4) f(x) = x + 1 𝑥
Have your completed HW out for a stamp

3. Today’s Agenda Practice Graphing Transformations in Functions
y = x2
y = |x|
x2 + y2 = 1
Transformations in Functions
Vertical Shifts
Horizontal Shifts
Stretching
Shrinking
Announcements
PTC EC
CPT SLCC

4. Parabola
Fill in x,y table for y=x2 x y -2 -1 1 2

5. Absolute Value
Fill in x,y table for y=|x| x y -2 -1 1 2

6. Circle
x2 + y2 = 1

7. Vertical Shifts
Adding or subtracting numbers shifts the graph up or down.
f(x) = x2
f(x) = x2 + 1
f(x) = x2 – 2

8. Horizontal Shifts
Adding or subtracting numbers from x shifts the graph horizontally.
y = |x|
y = |x – 1|
y = |x + 3|

9. Notes Example
y = f(x) + 1
y = f(x) -2
y = f(x + 1)
y = f(x – 2)

10. Notes Example
y = x2 + 1
y = |x| - 3
y = (x – 2)2
y = (x – 1)2 - 2

11. Vertical Stretching y = c*f(x) multiply y coordinates by c
if c > 1, vertical stretch
if c < 1, vertical shrink
if c is negative, the graph is reflected across the x-axis
multiply y coordinates by c
y = x2
y = 2x2
y = ½x2
y = -x2

12. Notes Example y = 2f(x) y = -f(x) y = 1 2 f(x) y = -3f(x)

13. Horizontal Stretching
y = f(c*x)
if c > 1 horizontal stretch
if c <1 horizontal shrink
if c is negative, the graph is reflected across the y-axis.
multiply the x coordinates by c

14. Notes Example
y = f(2x)
y = f(½x)
y = f(-x)
y = f(-3x)
y = f(2x) – 1

15. Homework
9.2 pg 393 #1-24 all
9.3 pg 398 #1 – 53 odd
Use graph paper