1-6
Relations and Functions
Objectives
Identify the domain and range of relations
and functions.
Determine whether a relation is a function.
Vocabulary Words
Relation and
Function
Vertical Line Test
Domain and Range
Holt Algebra 2
1-6
Relations and Functions
A relation is a pairing of input values with
output values. It can be shown as a set of
ordered pairs (x,y), where x is an input and
y is an output.
The set of input (x) values for a relation is
called the domain, and the set of output
(y) values is called the range.
Holt Algebra 2
1-6
Relations and Functions
Mapping Diagram
Domain
Range
A
2
B
C
Set of Ordered Pairs
{(2, A), (2, B), (2, C)}
(x, y)
Holt Algebra 2
(domain, range)
1-6
Relations and Functions
Example 1: Identifying Domain and Range
Give the domain and range for this relation:
{(100,5), (120,5), (140,6), (160,6), (180,12)}.
List the set of ordered pairs:
{(100, 5), (120, 5), (140, 6), (160, 6), (180, 12)}
Domain: {100, 120, 140, 160, 180} The set of x-coordinates.
Range: {5, 6, 12}
Holt Algebra 2
The set of y-coordinates.
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Relations and Functions
Example 2
Give the domain and range for the relation
shown in the graph.
List the set of ordered pairs:
{(–2, 2), (–1, 1), (0, 0),
(1, –1), (2, –2), (3, –3)}
Domain: {–2, –1, 0, 1, 2, 3} The set of x-coordinates.
Range: {–3, –2, –1, 0, 1, 2} The set of y-coordinates.
Holt Algebra 2
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Relations and Functions
Not a function: The relationship
from number to letter is not a
function because the domain value 2
is mapped to the range values A, B,
and C.
Function: The relationship from
letter to number is a function
because each letter in the domain is
mapped to only one number in the
range.
Both functions and non-functions are relations!
Holt Algebra 2
1-6
Relations and Functions
Holt Algebra 2
1-6
Relations and Functions
Example 3A: Using the Vertical-Line Test
Use the vertical-line test to determine
whether the relation is a function. If not,
identify two points a vertical line would pass
through.
This is a function. Any vertical
line would pass through only
one point on the graph.
Holt Algebra 2
1-6
Relations and Functions
Example 3B Using the Vertical-Line Test
Use the vertical-line test to determine whether
the relation is a function. If not, identify two
points a vertical line would pass through.
This is a function. Any vertical
line would pass through only
one point on the graph.
Holt Algebra 2
1-6
Relations and Functions
Example 3C: Using the Vertical-Line Test
Use the vertical-line test to determine
whether the relation is a function. If not,
identify two points a vertical line would pass
through.
This is not a function. A vertical
line at x = 1 would pass through
(1, 1) and (1, –2).
Holt Algebra 2
1-6
Relations and Functions
Function: The relationship is a function if each member of
the domain is mapped to only one number in the range.
Example 4A: Is this relation a function?
From graph or ordered pairs:
{(–2, 2), (–1, 1), (0, 0),
(1, –1), (2, –2), (3, –3)}
Holt Algebra 2
1-6
Relations and Functions
Function: The relationship is a function if each member of
the domain is mapped to only one number in the range.
Example 4B: Is this relation a function?
{(100,5), (120,5), (140,6), (160,6), (180,12)}.
Identify the domain and range:
Domain: {100, 120, 140, 160, 180}
Range: {5, 6, 12}
Holt Algebra 2
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Relations and Functions
Example 4C: Is this relation a function?
A.
There is only one price for
each shoe size. The relation
from shoe sizes to price
makes is a function.
B. Names in a classroom and grades
C. (Reverse B…) from class grades, find student
name.
Holt Algebra 2
1-6
Relations and Functions
Example 5A: Is this relation a function?
Use the vertical-line test to determine whether
the relation is a function. If not, identify two
points a vertical line would pass through.
This is not a function. A vertical
line at x = 1 would pass
through (1, 2) and (1, –2).
Holt Algebra 2
1-6
Relations and Functions
Example 5B: Is this relation a function?
Use the vertical-line test to determine
whether the relation is a function. If not,
identify two points a vertical line would pass
through.
not a function
Holt Algebra 2