Algebra 2 Warm up5.13.13

Complete the table below, if y = 4 - 2x

X Y ( X , Y )

-1

0

1

2

3

y = 4 - 2x

X Y ( X , Y )

-1 6 (-1 , 6)

0 4 (0 , 4)

1 2 (1 , 2)

2 0 (2 , 0)

3 -2 (3 , -2)

y = 4 - 2x

Vocabulary

• Function: Rule that assigns each input value to exactly one output.

Usually we describe a function with an equation.

Grading Function

Vocabulary

• Function: Rule that assigns each input value to exactly one output.

Usually we describe a function with an equation.

• Domain: x –values, or input values.

• Range: y – values , or output values.

How do we know if a graph is a function?

• If it passes THE VERTICAL LINE TEST

The vertical line test

1. Move a vertical line across the entire graph from left to right.

2. If it intersects the graph only ONCE in all locations, then it is a function.

Is this a function?

Is this a function?

Is this a function?

What is the Domain and Range?

What is the Domain and Range?

What is the Domain and Range?

Function notation

)(xf

Practice1. Is a function represented? If so what is the

domain and range.

a. (2,-4) (4,4) (6,-1) (5,0) (1,6) (2,4) (3, -2)

b.

2. If , then find f (0) , f (-2) , and f (3a)5)( 2xxf

Finding the domain from the equation

Example: What is the domain of the function given by

Functions only have real number outputs.Anything that gives an imaginary number or a zero denominator is a restriction.

How to find the domain:Assume that the domain is the set of all real numbers except for the restrictions.

5)( xxf

Examples

• What is the domain?

• What is the domain?

7

2)(

xxf

9

7)(

2xxf

More challenging examples

• What is the domain?

• What is the domain?

4

32)(

xxxf

6

9)(

x

xxf

Practice• What is the domain?

• What is the domain?

• What is the domain?

xxxf

5

5)(

2

7)( 2xxf

3 7)( xxf