Problem 10 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The interval \([-5, \infty)\) in set-builder notation is \(x | -5 \leq x < \infty\). It can be graphed on a number line by coloring in the point at -5 and drawing a line from this point that extends towards positive infinity.

Step 1: Set-Builder Notation

Set-builder notation is another way to express the range of values. In set-builder notation, the given interval \([-5, \infty)\) can be written as \(x |-5 \leq x < \infty\) which means that x is any element such that x is greater than or equal to -5 but less than infinity. In other words, x can take on any value from -5, inclusive, to positive infinity.

Step 2: Graph on a Number Line

To graph the interval \([-5, \infty)\) on a number line, a line is drawn to represent the number line. A point is drawn on this line to denote -5. Because -5 is inclusive, this point is colored in (or a solid circle is drawn). Then a line is drawn from this point and extends towards positive infinity. This shows that all values greater than or equal to -5 are included in the set.