2.3 – Introduction to Functions

• Objectives:– State the domain and range of a relation, and

tell whether it is a function.– Write a function in function notation and

evaluate it.

• Standards: – 2.8.11.S. Analyze properties and relationships

of functions.– 2.8.11.O. Determine the domain and range of

a relation.

Warm Up:

- 7 3 16

- 1.44 - 8 0.001

The domain of a function is the set of all possible values of x (the inputs).

The range of a function is the set of all possible values of y (the outputs).

Examples: State whether the data in each table represents a function.

a). b).

a).

b).

More Examples:

x y

3 4

3 5

5 -4

6 3

Ex. 1c

NO

x y

2 2

4 3

6 4

8 5

Ex. 1d

YES

c).

Not a function. It does not pass the vertical line test.

d).

Not a function. It does not pass the vertical line test.

The domain of a function is the set of all possible values of x (the inputs).

The range of a function is the set of all possible values of y (the outputs).

Domain: {-2, 0, 3, 8}Range: {-26, -6, 24, 74}

Domain: {-6, -4, 2, 3}Range: {7, 12, 19, 39}

• III. A function is a special type of relation. A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation.

Ex 4.

D:

R:

b.

2x

0y

State the domain and range of eachgraphed.

c.d.

D: x > -2

R: y > -1

Open circle

Functions and Function Notationy = 2x + 5 → f (x) = 2x + 5

If there is a correspondence between the domain

and range that is a function, then y = f(x), and (x, y)

can be written as (x, f(x)). The number represented by f(x) is the value of the function f at x.

The variable x is called the independent variable.

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

p. 108: #17-35 odd (answers in back of book)

p. 108: #17-35 odd (answers in back of book)

pp. 108 &109: 37-47odd

p. 109: #51, 53, 57

Homework