This document defines and provides examples of the domain and range of a function. The domain is the set of all independent variable (x-coordinate) values, while the range is the set of all dependent variable (y-coordinate) values. Several examples of identifying the domain and range of functions given their sets of ordered pairs are provided. The document also discusses using the vertical line test to determine if a graph represents a function.

1. Domain & RangeDomain & Range

2.  A function is a set of ordered pairs ofA function is a set of ordered pairs of
numbers (x, y) such that no x –valuesnumbers (x, y) such that no x –values
are repeated.are repeated.
 What are the domain and range of aWhat are the domain and range of a
function?function?
 The domain and range of a function areThe domain and range of a function are
sets that describe those ordered pairs.sets that describe those ordered pairs.

3. DefinitionDefinition ExampleExample
{(3, 6), (2, 8), (5,{(3, 6), (2, 8), (5,
3)}3)}
DomainDomain All the x-coordinates inAll the x-coordinates in
the function's orderedthe function's ordered
pairspairs
{ 3, 2, 5}{ 3, 2, 5}
RangeRange All the y-coordinates inAll the y-coordinates in
the function's orderedthe function's ordered
pairspairs
{ 6, 8, 3}{ 6, 8, 3}

4. The domain is the set of all the values ofThe domain is the set of all the values of
the independent variable, the x-the independent variable, the x-
coordinatecoordinate
The range is the set of all the values ofThe range is the set of all the values of
the dependent variable, the y-the dependent variable, the y-
coordinate.coordinate.

5. Identify the domain and range of theIdentify the domain and range of the
function below.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}

6. What is the domain of this function?What is the domain of this function?
What is the range of this function?What is the range of this function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5

7. The graph shows the path of a golf ballThe graph shows the path of a golf ball
What is the range
of this function?
F 0 < y < 100
G 0 ≤ y ≤ 100
H 0 ≤ x ≤ 5
J 0 ≤ x ≤ 5

8. What is the domain of this function?What is the domain of this function?
A -1 ≤ x ≤ 5
B -1 ≤ x ≤ 9
C 2 ≤ x ≤ 5
D 0 ≤ y ≤ 9

9. What is the domain of the functionWhat is the domain of the function
shown on the graph?shown on the graph?
A -2 < y ≤ 2
B -4 ≤ x ≤ 6
C -4 < y ≤ 2
D -2 < x ≤ 6

10. The Vertical Line TestThe Vertical Line Test
The vertical line test is used toThe vertical line test is used to
determine if a graph is a function.determine if a graph is a function.

11. 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.