Problem 4 - College Algebra Essentials

Question

Express each interval in set-builder notation and graph the interval on a number line. $$[-4,3)$$

Step-by-Step Solution

Answer

In set-builder notation, the interval [-4,3) is expressed as {x | -4 ≤ x < 3}. For the graph, a line connecting a filled circle at -4 and an open circle at 3 is drawn on a number line.

Step 1: Express the interval in set-builder notation

The interval [-4,3) represents the set of all real numbers x, such that -4 ≤ x < 3. In set-builder notation, it’s expressed as {x | -4 ≤ x < 3}

Step 2: Graphing the interval on a number line

On a number line, indicate -4 and 3. A filled circle is used at -4 because it's included while an open circle is used at 3 because it's not included. Draw a line between the two circles, making sure to include -4 and exclude 3.