4-2 Relations and Functions
Warm Up
Generate ordered pairs for the function
y = x + 3 for x = 2, 1, 0, 1, and 2.
Find the y values, and put them together as
an ordered pairs as (x,y)
x
(x,y)
-2
(2, 1)
y=x+3
=-2 + 3
=1
-1
(1, 2)
y=x+3
= -1 + 3
=2
(0, 3)
y=x+3
=0+3
=3
(1, 4)
y=x+3
=1+3
=4
(2, 5)
y=x+3
=2+3
=5
Holt Algebra 1
4-2 Relations and Functions
Objectives
Identify functions.
Find the domain and range of relations and
functions.
Holt Algebra 1
4-2 Relations and Functions
Showing Multiple
Representations of Relations
Example 1:
Express the relation {(2, 3), (4, 7), (6, 8)}:
1. as a table,
2. as a graph,
3. and as a mapping diagram.
Holt Algebra 1
4-2 Relations and Functions
1. Represent as Table:
x y
x y
{(2, 3), (4, 7), (6, 8)}
Table
Holt Algebra 1
Write all x-values under x
and write all y-values under y.
4-2 Relations and Functions
2. Represent as Graph:
{(2, 3), (4, 7), (6, 8)}
Graph
(4,7)
(2,3)
Holt Algebra 1
(6,8)
Use the x- and y-values to
plot the ordered pairs.
4-2 Relations and Functions
3. Represent as Mapping Diagram:
{(2, 3), (4, 7), (6, 8)}
Mapping Diagram
Holt Algebra 1
Write all x-values under x and
all y-values under y. Draw an
arrow from each x-value to its
corresponding y-value.
4-2 Relations and Functions
Your turn to try it!!! PRACTICES
Express the relation {(1, 3), (2, 4), (3, 5)} as
a table, as a graph, and as a mapping diagram.
Table
Graph
Mapping Diagram
y
x
Holt Algebra 1
4-2 Relations and Functions
The domain of a relation is the set
of first coordinates (or x-values) of
the ordered pairs.
The range of a relation is the set
of second coordinates (or y-values)
of the ordered pairs.
Holt Algebra 1
4-2 Relations and Functions
Remember this way:
y
Range
my EX WIFE is a DR.
X
Holt Algebra 1
Domain
4-2 Relations and Functions
Check It Out! Example 2a
Give the domain and range of the relation.
6
5
2
1
Holt Algebra 1
1
0
Domain: {6, 5, 2, 1}
Range: {4, 1, 0}
4-2 Relations and Functions
Check It Out! Example 2b
Give the domain and range of the relation.
Holt Algebra 1
Domain: {1, 4, 8}
Range: {1, 4}
4-2 Relations and Functions
A function is a special type of relation
that pairs each domain value with
exactly one range value.
Notes:
If it is a function, then none of x
(domain) value should be repeated
Holt Algebra 1
4-2 Relations and Functions
Example 3A: Identifying Functions
Give the domain and range of the relation. Tell
whether the relation is a function. Explain.
{(3, 2), (5, 1), (4, 0), (3, 1)}
The relation is not a function. Each domain value
does not have exactly one range value.
The domain value 3 is repeated, paired with the
range values 2 and 1.
Holt Algebra 1
4-2 Relations and Functions
Example 3B: Identifying Functions
Give the domain and range of the relation. Tell
whether the relation is a function. Explain.
4
8
4
{(-4, 2), (-8, 2), (4, 1), (5, 1)}
5
This relation is a function. Each domain value is
paired with exactly one range value.
Holt Algebra 1
4-2 Relations and Functions
Example 3C: Identifying Functions
Give the domain and range of the relation. Tell
whether the relation is a function. Explain.
(-3,1)
(-3,-2)
Draw in lines to see
the domain and range
values
Check out the points
that the line cut
through the plane
The relation is not a function. Nearly all domain
values have more than one range value.
Holt Algebra 1
