IDENTIFYING FUNCTIONS

In the following examples, give the domain and range of each relation. Tell whether the relation is a function. Explain.

Example 1 :

Solution :

Domain  =  {75, 68, 125}

Range  =  {2, 3}

(Even though 2 appears twice in the table, it is written only once when writing the range)

This relation is a function. Each domain value is paired with exactly one range value.

Example 2 :

Domain  =  {7, 9, 12, 15}

Range  =  {-7, -1, 0}

Use the arrows to determine which domain values correspond to each range value.

This relation is not a function. Each domain value does not have exactly one range value. The domain value 7 is paired with the range values -1 and 0.

Example 3 :

Solution :

Draw lines to see the domain and range values.

The domain is all x-values from -4 through 4, inclusive.

Domain : -4 ≤ x ≤ 4

The range is all y-values from -4 through 4, inclusive.

Range : -4 ≤ y ≤ 4

To compare domain and range values, make a table using points from the graph.

This relation is not a function because there are several domain values that have more than one range value. For example, the domain value 0 is paired with both 4 and -4.

Example 4 :

{(8, 2), (-4, 1), (-6, 2), (1, 9)}

Solution :

Domain  =  {8, -4, 6, 1}

Range  =  {2, 1, 9}

This relation is a function. Each domain value is paired with exactly one range value.

Example 5 :

Solution :

Domain  =  {4, 3, 2}

Range  =  {-5, -4, -3}

This relation is not a function. Each domain value does not have exactly one range value. The domain value 2 is paired with the range values -5 and -4.

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