1. Objective: I can understand transformations of functions.
Families of Functions
Objective:
I can understand transformations of functions.

2. Vocabulary Parent Function Simplest form in a set of functions.
Transformation:
Change in the size or position of a function
Translation:
Moves a function horizontally or vertically
Reflection:
Reflects a function across a line of reflection
Dilation:
Changes a function size
Domain:
Set of all input values (x values)
Range:
Set of all output values (y values)

3. 4 Parent Functions Absolute Value Quadratic 𝑦= 𝑥
Domain: all real numbers
Domain: all real numbers
Range: y 0 ≥
Range:
𝑦 ≥0

4. Square Root Cubic 𝑦= 𝑥 Domain: 𝑥 ≥0 Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 Range:
𝑦= 𝑥
Domain:
𝑥 ≥0
Domain:
𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Range:
𝑦 ≥0
Range:
𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

5. Dilations x y1 y2 -2 2 4 -1 1 Dilations: Vertical stretch compression
Graph x y1 y2 -2 2 4 -1 1
Dilations: Vertical
stretch compression

6. Translations Set your calculator window to: Graph x y1 y2 3 1 4 2 7 93 1 4 2 7 9 12
Vertical Translation: k units
Up: Down:

7. Reflections x y1 y3 -2 error 1.4 -1 1 2 x y1 y2 1 -1 2 1.4 -1.4 3 1.7
Graph x y1 y3 -2
error
1.4 -1 1 2 x y1 y2 1 -1 2
1.4
-1.4 3
1.7
-1.7
Reflections:
Across x-axis
Across y-axis

8. Transformation of f(x)
= 𝑥
Translation: Horizontal (k > 0)
Translation: Vertical (k > 0)
Right h units
𝑓 𝑥−ℎ
Up k units
𝑓 𝑥 +𝑘
𝑓 𝑥+ℎ
𝑓 𝑥 −𝑘
Left h units
Down k units
𝑥−ℎ
𝑥 +𝑘
Reflection
Dilation: Vertical by a factor of a
𝑎⋅𝑓 𝑥
𝑎 𝑥
Across x-axis
−𝑓 𝑥
− 𝑥
Stretch:
𝑎>1
𝑓 −𝑥
Across y-axis
Compression:
N/A
0<𝑎<1
𝑦=±𝑎 𝑥−ℎ +𝑘