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Chapter 1: Problem 2

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

Short Answer

Expert verified
In set-builder notation, the interval (-2,4] is written as \( \{ x \: | \: -2 < x \leq 4 \} \). On the number line, it is represented by a line segment starting with an open circle at -2 and ending with a filled circle at 4.

Step by step solution

01

Converting to set-builder notation

The given interval is (-2,4]. In set-builder notation, this can be written as \( \{ x \: | \: -2 < x \leq 4 \} \). Here, x is the variable representing any number within the interval, and the vertical bar: '|' signifies 'such that'.
02

Translating the interval to a number line

To represent this interval on a number line, a circle is drawn on -2 and 4, indicating these are the boundary points. The circle at -2 is open which means -2 is not included in the interval, while the circle at 4 is filled indicating that 4 is included. Lastly, a line segment joining these circles is drawn to show the range of the interval.

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