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Chapter 0: Problem 4

Express each interval in set-builder notation and graph the interval on a number line. $$[-5,2)$$

Short Answer

Expert verified
The interval \([-5,2)\) is written in set-builder notation as \(\{x \in \mathbb{R}: -5 \leq x < 2\}\). The number line is shaded from -5 (included) to 2 (excluded).

Step by step solution

01

Understand the Interval

The interval \([-5,2)\) includes all real numbers between -5 and 2, including -5 but excluding 2.
02

Write in Set-Builder Notation

Now, it can be put into the set-builder notation. In that notation, this set is \(\{x\in \mathbb{R}: -5 \leq x < 2\}\). This means the set of all real numbers x such that x is greater than or equal to -5 and less than 2.
03

Graph the Interval on a Number Line

Draw a number line from about -6 to 3. Place a closed circle at -5, to illustrate it's included in the set, and an open circle at 2, to illustrate it's not included in the set. Shade the number line from -5 to 2, not including 2.

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