```PRE-ALGEBRA
Lesson 8-1 Warm-Up
PRE-ALGEBRA
Relations and Functions (8-1)
What is a relation?
relation: a set of ordered pairs
Example: The (age, height) ordered pairs below form a relation.
You can list the set of ordered pairs in a relation using braces --- {}
{(18, 4.0), (16, 4.5), (20, 5.5), 14, 5.0)}
What is the “domain” of
a relation?
domain: the set (group) of all of the x-coordinates of a relation listed in
order from least to greatest
Example: The domain of the above relation is (14, 16, 18, 20)
What is the “range” of a
relation?
range: the set (group) of all of the y-coordinates of a relation listed in
order from least to greatest
Example: The range of the above relation is (4.0, 4.5, 5.0, 5.5)
What is a mapping
diagram?
mapping diagram: a diagram in which the domain values are matched
with their range values using arrows
Example: The following is a mapping diagram of the above giraffe
relation.
PRE-ALGEBRA
Relations and Functions (8-1)
What is a function?
function: a relation in which each value in the range matches up with
exactly one value in the range (in other words, there aren’t two or more
coordinates with the same y-coordinate).
Examples: The mapping diagram on the left is a function, because no
value in the domain corresponds (matches up to), more than one range
value. The mapping diagram on the right is NOT a function, because
there are two range values for the domain value of 1.
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
Is each relation a function? Explain.
a. {(0, 5), (1, 6), (2, 4), (3, 7)}
List the domain values and the range values
in order.
Draw arrows from the domain values to their
range values.
There is one range value for each domain value. This relation
is a function.
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
(continued)
b. {(0, 5), (1, 5), (2, 6), (3, 7)}
There is one range value for each domain value. This relation
is a function.
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
(continued)
c. {(0, 5), (0, 6), (1, 6), (2, 7)}
There are two range values for the domain value 0.
This relation is not a function.
PRE-ALGEBRA
Relations and Functions (8-1)
How do you create a
mapping diagram?
To create a mapping diagram, list the domain and range values in order.
Then, draw arrows from the domain values to their range values.
Example: Is the relation [(0,1), (1,2), (1,3), (2,4)} a function?
List the domain and range values in order
Draw arrows from the domain values to
their range values.
The relation is a function, because there is only one range value for
each domain value.
What is the vertical line
test?
Vertical-Line Test: On a graph, if a vertical (up-down) line passes
through more than one coordinate, that means that at least one xcoordinate shares more than one y-coordinate, which means the relation
is not a function (in other words, a relation that doesn’t pass the vertical
line test is not a function).
PRE-ALGEBRA
Relations and Functions (8-1)
Example: The following relation is not a function, because a vertical line
(like a pencil) passes through (3,0) and (3,2).
How do you use the
vertical line test?
To use the vertical line test, graph the function to determine whether a
vertical line will pass through two or more points.
Example: Use the vertical line test to determine if the following table is a
function.
1. Graph the
function.
2. Determine if
a vertical line
will pass
through two or
more like..
The relation is not a function, because a vertical line
would pass
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
Is the time needed to mow a lawn a function of
the size of the lawn? Explain.
No; two lawns of the same size (domain value)
can require different lengths of time (range values)
for mowing.
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
a. Graph the relation shown in the table.
Domain
Value
–3
–5
3
5
Range
Value
5
3
5
3
Graph the ordered
pairs (–3, 5), (–5, 3),
(3, 5), and (5, 3).
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
(continued)
b. Use the vertical-line test. Is the relation a function?
Explain.
Pass a pencil across the graph as shown.
Keep the pencil vertical (parallel to the
y-axis) to represent a vertical line.
The pencil does not pass through two points at any one of its
positions, so the relation is a function.
PRE-ALGEBRA
Relations and Functions
LESSON 8-1
Lesson Quiz
Is each relation a function? Explain.
1. {(–2, –1), (4, 2), (–8, –4), (6, 3)}
Yes; there is only one range value for each domain value.
2. {(5, 0), (7, 2), (9, 4), (5, 1)}
No; the domain value 5 has two range values, 0 and 1.
3. Graph the relation in the table.
Is the relation a function?
Explain.
Yes; there is one range value for
each domain value. Check students’ graphs.
x
–1
y
7
0
1
7
7
2
7
PRE-ALGEBRA
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