Warm-UpEvaluate each expression.

1) x – 2, for x = -5

2) -2x, for x = -1.5

3) x2, for x = -4

4) -x2, for x = -1.2

5) x3, for x = -2

6) -x3, for x = -0.1

4 minutes

2.3 Intro to Functions2.3 Intro to Functions2.3 Intro to Functions2.3 Intro to FunctionsObjectives: •State the domain and range of a relation, and tell whether it is a function•Write a function in function notation and evaluate it

Definition of a Function

Function: each value of the first variable is paired with exactly one value of the second variable

Domain: set of all possible values of the first variable

Range: set of all possible values of the second variable

Example 1

x y

2 2

4 3

6 4

8 5

State whether the data in each table represents y as a function of x. Explain.

x y

3 4

3 5

5 -4

6 3

function not a function

Vertical-Line TestIf every vertical line intersects a given graph at no more than one point, then the graph represents a function.

function not a function

Definition of a RelationRelation: each value of the first variable

is paired with one or more values of the second variable

Domain: set of all possible values of the first variable

Range: set of all possible values of the second variable

Example 2State the domain and range of the relation, and state whether it is a function.{ (–7, 5), (4, 12), (8, 23), (16, 8) }

domain: { –7, 4, 8, 16}range: { 5, 8, 12, 23 }

This is a function because each x-coordinate is paired with only one y-coordinate.

Function NotationIf there is a correspondence between values of the domain, x, and values of the range, y, that is a function, then y = f(x), and (x,y) can be written as (x,f(x)).

The variable x is called the independent variable.The variable y, or f(x) is called the dependent variable.

Example 3

f(–1) = –2.5 (–1) + 11f(–1) = 2.5 + 11

f(–1) = 13.5

Evaluate f(x) = –2.5x + 11, where x = –1.

Example 4A gift shop sells a specialty fruit and nut mix at a cost of $2.99 per pound. During the holiday season, you can buy as much of the mix as you like and have it packaged in a decorative tin that costs $4.95.a) Write a linear function to model the total cost in dollars, c, of the tin containing the fruit and nut mix as a function of the number of pounds of the mix, n.

c(n) =

4.95 + 2.99n b) Find the total cost of a tin that contains 1.5

pounds of the mix.c(n) = 4.95 + 2.99n

c(1.5) = 4.95 + 2.99(1.5)c(1.5) = 9.44

$9.44

Homework

p.107 #17-49 odds