In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 5, 2)

Key Concepts

Interval Notation

Interval notation is a mathematical notation used to represent a range of numbers. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, the interval [-5, 2) includes -5 but excludes 2, meaning all numbers from -5 up to, but not including, 2.

Set-Builder Notation

Set-builder notation is a concise way to express a set by specifying a property that its members must satisfy. It typically takes the form {x | condition}, where 'x' is a variable and 'condition' describes the constraints on 'x'. For the interval [-5, 2), the set-builder notation would be {x | -5 ≤ x < 2}.

Graphing Intervals on a Number Line

Graphing intervals on a number line visually represents the range of values included in the interval. Closed endpoints are marked with a solid dot, indicating inclusion, while open endpoints are marked with an open circle, indicating exclusion. For the interval [-5, 2), you would place a solid dot at -5 and an open circle at 2, shading the region in between.