Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 3.10, Problem 19WE
To determine

To find:the domain of the given relation and draw the function also whether the relation is a function or not.

Expert Solution & Answer
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Answer to Problem 19WE

The domain of relation is {2,1, 1, 2} and the relation is not a function.

Explanation of Solution

Given information:

The relation is {(x,y): |x|y=2} where x and y are integer.

Definition used:

A function is relation in which different ordered pairs has different first coordinates.

Result used:

Vertical line test:

A relation is a function if and only if no vertical line intersects its graph more than once.

Calculation:

It is given that the relation is {(x,y): |x|y=2} where x and y are integer.

The term |x|y=2 can be written as |x|=2y .

Note that, the modulus of x defines as |x|={x         if x0x      if x<0}

By using the definition of the modulus, x=2y or x=2y .

If the value of x=2y ,

The value of x and y are integers, so the value of y cannot be 0, more than 2 and less than

  2 .

Thus, the only possible values of y are 2, 1, 1,and 2 .

The ordered pairs of the elements are (2,1), (1,2), (1,2), (2,1) such that x=2y .

If the value of x=2y , the only possible values of y are 2, 1, 1,and 2 .

The ordered pairs of the elements are (2,1), (1,2), (1,2), (2,1) such that x=2y .

Thus, the relation is a set of ordered pairs as listed below,

{ (2,1), (1,2), (1,2), (2,1) , (2,1), (1,2), (1,2), (2,1) }

Note that, the domain of the relation is a set of first coordinates in the ordered pairs.

Therefore, the domain of relation is {2,1, 1, 2} .

A function is relation in which different ordered pairs has different first coordinates.

Here, the different ordered pairs (1,2), and (1,2) has a same first coordinate.

Therefore, the given relation {(x,y): |x|y=2} is not a function.

Graph:

The graph of the relation {(x,y): |x|y=2} as shown in Figure 1,

  Algebra and Trigonometry: Structure and Method, Book 2, Chapter 3.10, Problem 19WE

From Figure 1, it is observed that the vertical line passing through 1 intersects more than one points so it cannot satisfy the vertical line test.

Therefore, the relation is not function.

Chapter 3 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 3.1 - Prob. 11OECh. 3.1 - Prob. 1WECh. 3.1 - Prob. 2WECh. 3.1 - Prob. 3WECh. 3.1 - Prob. 4WECh. 3.1 - Prob. 5WECh. 3.1 - Prob. 6WECh. 3.1 - Prob. 7WECh. 3.1 - Prob. 8WECh. 3.1 - Prob. 9WECh. 3.1 - Prob. 10WECh. 3.1 - Prob. 11WECh. 3.1 - Prob. 12WECh. 3.1 - Prob. 13WECh. 3.1 - Prob. 14WECh. 3.1 - Prob. 15WECh. 3.1 - Prob. 16WECh. 3.1 - Prob. 17WECh. 3.1 - Prob. 18WECh. 3.1 - Prob. 19WECh. 3.1 - Prob. 20WECh. 3.1 - Prob. 21WECh. 3.1 - Prob. 22WECh. 3.1 - Prob. 23WECh. 3.1 - Prob. 24WECh. 3.1 - Prob. 25WECh. 3.1 - Prob. 26WECh. 3.1 - Prob. 27WECh. 3.1 - Prob. 28WECh. 3.1 - Prob. 29WECh. 3.1 - Prob. 30WECh. 3.1 - Prob. 31WECh. 3.1 - Prob. 32WECh. 3.1 - Prob. 33WECh. 3.1 - Prob. 34WECh. 3.1 - Prob. 35WECh. 3.1 - Prob. 36WECh. 3.1 - Prob. 37WECh. 3.1 - Prob. 38WECh. 3.1 - Prob. 39WECh. 3.1 - Prob. 40WECh. 3.1 - Prob. 1PCh. 3.1 - Prob. 2PCh. 3.1 - Prob. 3PCh. 3.1 - Prob. 4PCh. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.1 - Prob. 8PCh. 3.1 - Prob. 9PCh. 3.1 - Prob. 10PCh. 3.1 - 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Prob. 2MRECh. 3.9 - Prob. 3MRECh. 3.9 - Prob. 4MRECh. 3.9 - Prob. 5MRECh. 3.9 - Prob. 6MRECh. 3.9 - Prob. 7MRECh. 3.9 - Prob. 8MRECh. 3.9 - Prob. 9MRECh. 3.9 - Prob. 10MRECh. 3.9 - Prob. 11MRECh. 3.9 - Prob. 12MRECh. 3.9 - Prob. 13MRECh. 3.10 - Prob. 1OECh. 3.10 - Prob. 2OECh. 3.10 - Prob. 3OECh. 3.10 - Prob. 4OECh. 3.10 - Prob. 5OECh. 3.10 - Prob. 6OECh. 3.10 - Prob. 7OECh. 3.10 - Prob. 8OECh. 3.10 - Prob. 9OECh. 3.10 - Prob. 10OECh. 3.10 - Prob. 11OECh. 3.10 - Prob. 12OECh. 3.10 - Prob. 13OECh. 3.10 - Prob. 14OECh. 3.10 - Prob. 15OECh. 3.10 - Prob. 16OECh. 3.10 - Prob. 17OECh. 3.10 - Prob. 18OECh. 3.10 - Prob. 19OECh. 3.10 - Prob. 20OECh. 3.10 - Prob. 21OECh. 3.10 - Prob. 22OECh. 3.10 - Prob. 23OECh. 3.10 - Prob. 24OECh. 3.10 - Prob. 1WECh. 3.10 - Prob. 2WECh. 3.10 - Prob. 3WECh. 3.10 - Prob. 4WECh. 3.10 - Prob. 5WECh. 3.10 - Prob. 6WECh. 3.10 - Prob. 7WECh. 3.10 - Prob. 8WECh. 3.10 - Prob. 9WECh. 3.10 - Prob. 10WECh. 3.10 - Prob. 11WECh. 3.10 - Prob. 12WECh. 3.10 - Prob. 13WECh. 3.10 - Prob. 14WECh. 3.10 - Prob. 15WECh. 3.10 - Prob. 16WECh. 3.10 - Prob. 17WECh. 3.10 - Prob. 18WECh. 3.10 - Prob. 19WECh. 3.10 - Prob. 20WECh. 3.10 - Prob. 21WECh. 3.10 - Prob. 22WECh. 3.10 - Prob. 23WECh. 3.10 - Prob. 24WECh. 3.10 - Prob. 25WECh. 3.10 - Prob. 26WECh. 3.10 - Prob. 27WECh. 3.10 - Prob. 28WECh. 3.10 - Prob. 29WECh. 3.10 - Prob. 30WECh. 3.10 - Prob. 31WECh. 3.10 - Prob. 32WECh. 3.10 - Prob. 33WECh. 3.10 - Prob. 34WECh. 3.10 - Prob. 35WECh. 3.10 - Prob. 36WECh. 3.10 - Prob. 37WECh. 3.10 - Prob. 1STCh. 3.10 - Prob. 2STCh. 3.10 - Prob. 3STCh. 3.10 - Prob. 4STCh. 3.10 - Prob. 5STCh. 3.10 - Prob. 6STCh. 3.10 - Prob. 7STCh. 3.10 - Prob. 8STCh. 3.10 - Prob. 9STCh. 3.10 - Prob. 1ECh. 3.10 - Prob. 2ECh. 3.10 - Prob. 3ECh. 3.10 - Prob. 4ECh. 3.10 - Prob. 5ECh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CRCh. 3 - Prob. 15CRCh. 3 - Prob. 16CRCh. 3 - Prob. 17CRCh. 3 - Prob. 18CRCh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 1CLRCh. 3 - Prob. 2CLRCh. 3 - Prob. 3CLRCh. 3 - Prob. 4CLRCh. 3 - Prob. 5CLRCh. 3 - Prob. 6CLRCh. 3 - Prob. 7CLRCh. 3 - Prob. 8CLRCh. 3 - Prob. 9CLRCh. 3 - Prob. 10CLRCh. 3 - Prob. 11CLRCh. 3 - Prob. 12CLRCh. 3 - Prob. 13CLRCh. 3 - Prob. 14CLRCh. 3 - Prob. 15CLRCh. 3 - Prob. 16CLRCh. 3 - Prob. 17CLRCh. 3 - Prob. 18CLRCh. 3 - Prob. 19CLRCh. 3 - Prob. 20CLRCh. 3 - Prob. 21CLRCh. 3 - Prob. 22CLRCh. 3 - Prob. 23CLRCh. 3 - Prob. 24CLRCh. 3 - Prob. 25CLRCh. 3 - Prob. 26CLRCh. 3 - Prob. 27CLRCh. 3 - Prob. 28CLR
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