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Chapter 0: Problem 2

Express each interval in set-builder notation and graph the interval on a number line. $$(-2,4]$$

Short Answer

Expert verified
The set-builder notation for the interval (-2,4] is \( \{x \in \mathbb{R} : -2 < x 鈮� 4\}\). The graph of this interval on a number line involves a number line with a open circle at -2 (not included) and a filled circle at 4 (included), with a line connecting these two points.

Step by step solution

01

Convert into Set-Builder Notation

Set-builder notation involves describing a set by indicating the properties that its members must satisfy. In this case, the numbers are all real numbers \(x\) such that \(-2 < x 鈮� 4\). The set-builder notation will therefore be:- \( \{x \in \mathbb{R} : -2 < x 鈮� 4\}\)
02

Graph the interval on a number line

Draw a number line with -2 and 4 marked on it. Draw a circle at -2 to indicate that -2 is not included in the interval, and draw a filled circle at 4 to show that 4 is included. Draw a line connecting these two points.

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