1. Relations and Functions
PRE-ALGEBRA LESSON 8-1
(For help, go to Lesson 1-10.)
Graph each point.
1. A(3, 4) 2. B(–3, 1) 3. F(2, 0)
4. D(2, –2) 5. C(–4, –3) 6. E(0, –4)
Check Skills You’ll Need
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2. Relations and Functions
PRE-ALGEBRA LESSON 8-1
Solutions
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3. Relations and Functions
PRE-ALGEBRA 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.
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4. Relations and Functions
PRE-ALGEBRA 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.
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5. Relations and Functions
PRE-ALGEBRA 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.
Quick Check
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6. Relations and Functions
PRE-ALGEBRA 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.
Quick Check
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7. Relations and Functions
PRE-ALGEBRA LESSON 8-1
a. Graph the relation shown in the table.
Domain Value –3 –5 3 5
Range Value 5 3
Graph the ordered pairs
(–3, 5), (–5, 3), (3, 5), and (5, 3).
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8. Relations and Functions
PRE-ALGEBRA 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.
Quick Check
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9. Relations and Functions
PRE-ALGEBRA LESSON 8-1
Is each relation a function? Explain.
1. {(–2, –1), (4, 2), (–8, –4), (6, 3)}
2. {(5, 0), (7, 2), (9, 4), (5, 1)}
3. Graph the relation in the table.
Is the relation a function?
Explain.
Yes; there is only one range value for each domain value.
No; the domain value 5 has two range values, 0 and 1.
x y
–1 7
0 7
1 7
2 7
Yes; there is one range value for
each domain value. Check students’ graphs.
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