1. Functions and Transformations
Chapter 2.7
By Caitlyn McCall

2. Vocabulary
Family graph- a group of graphs that display one or more similar characteristics
Parent graph- graph of a parent function
Parent function- simplest graph in a family

3. Types of Functions
Constant
Linear or Identity
Absolute
Quadratic

4. Constant Function Straight horizontal line y = a
Domain= all real numbers
Range= the value of a

5. Linear or Identity Function
Straight diagonal line
y = x
Domain= all real numbers
Range= all real numbers

6. Absolute Value Function
Diagonal lines shaped like a V
f(x) = |x|
Domain= a set of real numbers
Range= a set of real numbers greater than or equal to 0

7. Quadratic Function Curved like a parabola f(x) = x²
Domain= set of real numbers
Range= set of real numbers greater than or equal to 0

8. Transformations of Functions
Translations
Reflections
Dilations (Wania)

9. Translations y = x² ± a moves up or down y = (x ± a)²
moves left or right

10. Reflections y = -x² reflects on the x axis y = (-x)²
reflects of the y axis

11. Dilations y = ax² a>1, graph stretches vertically
a<1, graph compresses vertically

12. Problem #1 Graph the function and describe the transformations
1. y = 2(x-2)²
Answer: Vertically stretched
Translated right 2 units

13. Problem #2 Graph the function and describe the transformations
2. y = -(x-3)² -5
Answer: Reflected on x axis
Translated right 3 units
Translated down 5 units

14. Problem #3 Select the correct equation for the function
y = x² -1
y = x² + 1
y = (x -1)²
y = (x +1)²
y = x² -1
y = x² + 1
y = (x -1)²
y = (x +1)²

15. Problem #4 Select the correct equation for the function
y = -|x+3|+6
y = -|x+6|+3
y = -|x+3|-6
y = -|x-3|+6
y = -|x+3|+6
y = -|x+6|+3
y = -|x+3|-6
y = -|x-3|+6