### Relations and Functions

```Extension
5.1
Relations and Functions
Lesson Tutorials
A relation pairs inputs with outputs. A relation that pairs each input with
exactly one output is a function.
Key Vocabulary
relation, p. 208
Vertical Line Test,
p. 209
EXAMPLE
Determining Whether Relations are Functions
1
Determine whether each relation is a function.
COMMON
CORE
a. (−2, 2), (−1, 2), (0, 2), (1, 0), (2, 0)
Functions
Every input has exactly one output.
In this extension, you will
● determine whether
relations are functions.
● use the vertical line test to
determine whether a graph
represents a function.
Learning Standards:
8.F.1
F.IF.1
F.IF.5
So, the relation is a function.
b.
Input
−2
−1
0
0
1
2
3
4
5
6
7
8
Output
The input 0 has two outputs, 5 and 6.
So, the relation is not a function.
c.
Input
Output
−9
−2
5
12
0
5
10
Every input has exactly one output.
So, the relation is a function.
Determine whether the relation is a function.
1. (−5, 0), (0, 0), (5, 0),
(5, 10), (10, 10)
2.
Input
Output
2
2.6
4
5.2
6
7.8
3. Input
1
2
—
Output
1
4
−—
0
1
4
—
Determine whether the statement is true or false. Explain your reasoning.
4. Every function is a relation.
5. Every relation is a function.
6. When you switch the inputs and outputs of any function, the resulting relation
is a function.
7. REASONING You record the number x of runs scored by the winning team and
the number y of runs scored by the losing team for each softball game in a
team’s season. Does the relation necessarily represent a function? Explain.
208
Chapter 5
MSCA_ALG1_PE_0501_ext.indd 208
Linear unctions
F
12/17/13 1:54:59 PM
You can use a vertical line test to determine whether a graph represents
a function.
Vertical Line Test
A graph represents a function when no vertical line passes
through more than one point on the graph.
Words
Examples Function
Not a function
y
y
x
Using the Vertical Line Test
2
EXAMPLE
x
Determine whether each graph represents a function.
a.
b.
y
6
y
6
5
5
4
4
3
3
2
2
1
1
0
0
1
2
3
4
5
6
0
7 x
You can draw a vertical line
through (2, 2) and (2, 5).
0
1
2
3
4
5
6
7 x
No vertical line can be drawn
through two points on the graph.
So, the graph does not
represent a function.
So, the graph represents
a function.
Determine whether the graph represents a function.
8.
y
6
9.
y
6
10.
y
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
0
0
0
1
2
3
4
5
6
7 x
0
1
2
3
4
5
6
7 x
0
0
1
2
3
4
5
6
7 x
11. REASONING You studied linear equations in Chapter 2. Do all linear equations