Unit 1, Part 2

Families of Functions, Domain & Range, Shifting

Functions What is a function? What are the different ways to

represent a function?

Important questions for the unit…

• What is a function?• What is domain?• What is range?

FunctionA 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)

Examples of a Function

{ (2,3) (4,6) (7,8)(-1,2)(0,4)} 4

-2

1

8

-4

2

4

-2

1

8

-4

2

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.

You Do: Is it a Function? Give the domain and range of each (whether it’s a function or not).

1.{(2,3) (2,4) (3,5) (4,1)}

2.{(1,2) (-1,3) (5,3) (-2,4)}

3. 4.

5.

0

-3

4

1

-5

9

Parent Functions

–F(x) = x–F(x) = x²–F(x) = x³ –F(x) = l x l–F(x) = √(x) –F(x) = 1

x

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

Shifting continued…

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

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

Piecewise Functions

• Give the domain and range of the following function.