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Representing Relations and Identifying Functions

This guide explains how to identify the domain and range of a relation, represent relations using graphs and mapping diagrams, and determine if a relation is a function.

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Representing Relations and Identifying Functions

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  1. The domain consists of all the x-coordinates:–2, –1, 1, 2,and3. The rangeconsists of all the y-coordinates:–3, –2, 1, and 3. EXAMPLE 1 Represent relations Consider the relation given by the ordered pair (– 2, –3), (– 1, 1), (1, 3), (2, – 2), and (3, 1). a.Identify the domain and range. SOLUTION

  2. b. Represent the relation using a graph and a mapping diagram. EXAMPLE 1 Represent relations SOLUTION b. Graph Mapping Diagram

  3. The relation isa function because each input is mapped onto exactly one output. a. Identify functions EXAMPLE 2 Tell whether the relation is a function. Explain. SOLUTION

  4. b. The relation isnota function because the input 1 is mapped onto both – 1 and 2. Identify functions EXAMPLE 2 Tell whether the relation is a function. Explain. SOLUTION

  5. for Examples 1 and 2 GUIDED PRACTICE 1. Consider the relation given by the ordered pairs (–4, 3), (–2, 1), (0, 3), (1, –2), and (–2, –4) a. Identify the domain and range. SOLUTION The domain consists of all the x-coordinates:–4, –2, 0 and 1, The rangeconsists of all the y-coordinates: 3, 1,–2 and –4

  6. for Examples 1 and 2 GUIDED PRACTICE b. Represent the relation using a table and a mapping diagram. SOLUTION

  7. 2. Tell whether the relation is a function. Explain. ANSWER Yes; each input has exactly one output. for Examples 1 and 2 GUIDED PRACTICE

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