7th Grade Math

Lesson 1B Rates and Functions 383

Relations and Functions

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Refer to the beginning of the lesson. The total cost (output) of the magazines

depends on, or is a function of, the number of magazines bought (input). The

number of magazines bought is called the independent variable because the

values are chosen and do not depend upon the other variable. The total cost

is called the dependent variable because it depends on the input value.

In a set of ordered pairs, the x-value is the independent variable, and the

y-value is the dependent variable.

Determine whether each relation is a function. Explain.

a. {(2, 1), (4, 3), (5, 4), (9, 7)} b. (^) x 2592
y 1473
Domain Range
2
4
5
9
1
3
4
7
Domain Range
2
5
9
1
3
4
7
The set of ordered pairs
is a function because each
x-value has only one
corresponding y-value.
This is not a function because
the x-value has two different
y-values.
Another way to determine whether a relation is a function is to
apply the vertical line test to the graph of the relation. Use a
pencil or straightedge to represent a vertical line.
Place the pencil at the left of the graph. Move it to the right
across the graph. If, for each value of x in the domain, the pencil
passes through only one point on the graph, then the graph
represents a function.
Determine whether the graph is a function. Explain your answer.
The graph represents a relation that is not a function because it
does not pass the vertical line test.
By looking at the graph, you can see that when x = 3, there are two
different y-values, 2 and 6.
0
y
0 x
377_384_C07_L1_895130.indd 383 12/31/09 4:23 PM