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Chapter 0: Problem 5

Express each interval in set-builder notation and graph the interval on a number line. $$[-3,1]$$

Short Answer

Expert verified
Set-builder notation: \({x | -3 \leq x \leq 1}\) ; on the number line, this interval is represented by a solid line from -3 to 1, inclusive.

Step by step solution

01

Convert to Set-Builder Notation

The interval \([-3,1]\) includes all real numbers \(x\) that are greater than or equal to -3 and less than or equal to 1. This can be written in set-builder notation as \({x | -3 \leq x \leq 1}\), which is read as 'the set of all \(x\) such that \(x\) is greater than or equal to -3 and \(x\) is less than or equal to 1.'
02

Plot on Number Line

To plot this interval on a number line, a straight horizontal line is drawn to represent the number line. A solid circle is drawn at -3 and another at 1, to represent that these numbers are included in the range of the interval. A solid line is drawn between these two points, to show that all numbers between -3 and 1 are also part of the interval. Numbers less than -3 or greater than 1 are left blank, as they are not included in the interval.

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