Domain & RangeDomain & Range

A function is a set of ordered A function is a set of ordered pairs of numbers (x, y) such pairs of numbers (x, y) such that no x –values are repeated. that no x –values are repeated.

What are the domain and range What are the domain and range of a function?of a function?

The domain and range of a The domain and range of a function are sets that describe function are sets that describe those ordered pairs.those ordered pairs.

DefinitionDefinition ExampleExample

{(3, 6), (2, 8), {(3, 6), (2, 8), (5, 3)}(5, 3)}

DomaDomainin

All the x-All the x-coordinates in the coordinates in the function's ordered function's ordered pairspairs

{ 3, 2, 5}{ 3, 2, 5}

RangRangee

All the y-All the y-coordinates in the coordinates in the function's ordered function's ordered pairspairs

{ 6, 8, 3}{ 6, 8, 3}

The domain is the set of all the The domain is the set of all the values of the independent values of the independent variable, the x-coordinatevariable, the x-coordinate

The range is the set of all the The range is the set of all the values of the dependent values of the dependent variable, the y-coordinate.variable, the y-coordinate.

Identify the domain and range Identify the domain and range of the function below.of the function below.

{ 2, 7), (4, 11), (6, 15), (8, 19)}{ 2, 7), (4, 11), (6, 15), (8, 19)}

The domain is { 2, 4, 6, 8}The domain is { 2, 4, 6, 8}

The range is { 7, 11, 15, 19}The range is { 7, 11, 15, 19}

What is the domain of this What is the domain of this function?function?

What is the range of this What is the range of this function?function?

Domain is 0 ≤ x ≤ 4

Range is 1 ≤ y ≤ 5

The graph shows the path of a golf The graph shows the path of a golf ballball

What is the range of this function?

F 0 < y < 100

G 0 ≤ y ≤ 100

H 0 ≤ x ≤ 5

J 0 ≤ x ≤ 5

What is the domain of this What is the domain of this

function?function?

A -1 ≤ x ≤ 5

B -1 ≤ x ≤ 9

C 2 ≤ x ≤ 5

D 0 ≤ y ≤ 9

What is the domain of the What is the domain of the function shown on the graph?function shown on the graph?

A -2 < y ≤ 2

B -4 ≤ x ≤ 6

C -4 < y ≤ 2

D -2 < x ≤ 6

The Vertical Line The Vertical Line TestTest

The vertical line test is used The vertical line test is used to determine if a graph is a to determine if a graph is a

function.function.

If a vertical line passes through a graph more than once, the graph is not the graph

of a function. Hint:

Pass a pencil across the graph held vertically to

represent a vertical line.The pencil crosses the

graph more than once. This is not a function

because there are two y-values for the same x-

value.