Unit 1, Part 2

1. Unit 1, Part 2 Families of Functions, Domain & Range, Shifting

2. Functions What is a function? What are the different ways to represent a function?

3. Important questions for the unit… • What is a function? • What is domain? • What is range?

4. A function is a mathematical “rule” that for each “input” (x-value) there is one and only one “output” (y – value). A function has a domain (input or x) and a range (output or y) Function

5. 8 -4 2 4 -2 1 Examples of a Function { (2,3) (4,6) (7,8)(-1,2)(0,4)}

6. 8 -4 2 4 -2 1 Non – Examples of a Function {(1,2) (1,3) (1,4) (2,3)} Vertical Line Test – if it passes through the graph more than once then it is NOT a function.

7. 1 -5 9 0 -3 4 You Do: Is it a Function? Give the domain and range of each (whether it’s a function or not). • {(2,3) (2,4) (3,5) (4,1)} • {(1,2) (-1,3) (5,3) (-2,4)} • 4. • 5.

8. Parent Functions • F(x) = x • F(x) = x² • F(x) = x³ • F(x) = l x l • F(x) = √(x) • F(x) = 1 x

9. Shifting Functions • On your graph paper, graph each parent function. • Graph the following functions (calc, table, however you’d like). • F(x) = x +3 • F(x) = x² + 3 and F(x) = (x + 3)² • F(x) = x³ -2 and F(x) = (x – 2)³ • F(x) = l x l – 4 and F(x) = l x – 4 l • F(x) = √(x) + 1 and F(x) = √(x + 1) • F(x) = 1 and F(x) = 1 - 2 x– 2 x

10. Shifting continued… • Looking at the graphs, in small groups see if you can come up with a rule for how graphs are shifted.

11. Shifting again… • Use your rule to graph these and describe how they are shifted. • F(x) = x -7 • F(x) = (x + 4)² - 2 • F(x) = (x – 2)³ + 6 • F(x) = l x – 5 l – 4 • F(x) = √(x + 10) + 3 • F(x) = 1 + 3 x– 8

12. Piecewise Functions • Give the domain and range of the following function.