1. Families of Functions, Domain & Range, Shifting
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?
Different ways to write domain and range (brackets, parentheses, etc)

4. Function
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)

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

6. Non – Examples of a Function4 -2 1 8 -4 2
{(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. {(2,3) (2,4) (3,5) (4,1)} {(1,2) (-1,3) (5,3) (-2,4)} 4. 5.
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. -3 4 1 -5 9

8. Parent Functions F(x) = x F(x) = x² F(x) = x³ F(x) = l x l F(x) = √(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 and F(x) = (x + 3)²
F(x) = x³ 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) = and F(x) =
x– 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) =
x– 8

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