Problem 6 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

In set-builder notation, the interval is written as \{x: -2 \leq x \leq 5\}. On the number line, it is visualized by shading or coloring the section of the line that includes all numbers between -2 and 5, including -2 and 5.

Step 1: Write in Set-Builder Notation

For the interval \([-2,5]\), it includes the numbers -2 and 5 i.e., both endpoints are inclusive. We can write this in set-builder notation as \{x: -2 \leq x \leq 5\}, which describes a set of all x such that x is greater than or equal to -2 and less than or equal to 5.

Step 2: Plot Interval on Number Line

Next, plot this interval on number line. Draw a line representing the number system and mark -2 and 5 on it. Because both -2 and 5 are included in the interval, shade or color both these points and also all the points lying between them on the line. This represents all the numbers between -2 and 5, inclusive.