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Chapter 3: Q.495 (page 360)

In the following exercise, use the graph of the relation to 鈸恖ist the ordered pairs of the relation 鈸慺ind the domain of the relation 鈸� find the range of the relation.

Short Answer

Expert verified

Order pairs of the relation are:

{(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}

Domain of the relation is,

{-3, -2, 0, 4}

Range of the relation is,

{-3, -1, 0, 1, 3, 4}

Step by step solution

01

 Step 1. Given information 

We have given graph is,

02

Step 2. Concept  

A relation is any set of ordered pairs, (x, y).

All the x-values in the ordered pairs together make up the domain.

All the y-values in the ordered pairs together make up the Range.

03

Part (a) Step 1. Explanation 

We have,

We know that,

A relation is any set of ordered pairs, (x, y).

From the graph we get order pairs of the relation are:

{(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}.

04

Part (a) Step 2. Conclusion 

Hence,

Order pairs of the relation are:

{(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}.

05

Part (b) Step 1. Explanation 

We have,

And order pairs are: {(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}

We knw that,

A relation is any set of ordered pairs, (x, y). All the x-values in the ordered pairs together make up the domain.

Therefore,

Domain of the relation is,

{-3, -2, 0, 4}.

06

Part (b) Step 2. Conclusion 

Hence, domain of the relation

{(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}

is, {-3, -2, 0, 4}.

07

Part (c) Step 1. Explanation 

We have,

and from the part " a " order pairs of the relation are:

{(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)}.

We know that, A relation is any set of ordered pairs, (x, y). All the y-values in the ordered pairs together make up the range.

Therefore,

Range of the relation is,

{-3, -1, 0, 1, 3, 4}.

08

Part (c) Step 2. Conclusion 

Hence,

Range of the relation {(-3, 1), (-2, -3), (-2, -1), (0, -1), (0, 4), (4, 3)} is,

{-3, -1, 0, 1, 3, 4}.

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