BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.1, Problem 64E
To determine

To graph: the given set.

Expert Solution

Explanation of Solution

Given information:

An interval is given as

  (,6](2,10)

Concept used:

An interval (a,b) in terms of an inequality can be expressed as a<x<b .

An interval [a,b] in terms of an inequality can be expressed as axb .

An interval [a,b) in terms of an inequality can be expressed as ax<b .

An interval (a,b] in terms of an inequality can be expressed as a<xb .

An interval (,b] in terms of an inequality can be expressed as xb .

An interval (,b) in terms of an inequality can be expressed as x<b .

An interval [a,) in terms of an inequality can be expressed as xa .

An interval (a,) in terms of an inequality can be expressed as x>a .

For any two or more sets, intersection of the sets gives the elements which are the only common elements of the sets. Intersection is represented by the symbol .

Calculation:

Consider the given interval.

  (,6](2,10)

Let us consider a variable x o express the inequality.

So, the interval can be expressed as an inequality as x62<x<10 .

Combining the interval will be 2<x6=(2,6]

Graph:

Now, graph the interval on number line as shown:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.1, Problem 64E

Here, 6 is included to the interval so, closed ball is placed for 6 on the number line.

Here, 2 is excluded from the interval so, open ball is placed for 2 on the number line.

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