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Chapter 0: Problem 9

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

Short Answer

Expert verified
The set-builder notation for the interval \([-3, \infty)\) is \(\{x \in \mathbb{R} : x \geq -3\}\). The graph of this interval on a number line starts at -3 (inclusive) and extends to the right, towards positive infinity.

Step by step solution

01

Translate into set-builder notation

The set-builder notation translates our interval into a mathematical expression of a set. The interval given is \([-3, \infty)\). This represents all real numbers that are greater than or equal to -3. In set-builder notation, we write this as: \[ \{x \in \mathbb{R} : x \geq -3\} \], where \(\mathbb{R}\) represents the set of all real numbers and \(x \geq -3\) represents the condition that all these numbers must meet.
02

Graph the interval on a number line

To made a graph on a number line, start by drawing a straight line to represent the number line. Then, mark a point on the line to represent -3. Draw a square bracket facing the number line at -3, indicating that -3 is included in the interval (because of the [ symbol in \([-3, \infty)\)). From -3, draw a ray to the right to represent all numbers greater than -3 upto \(\infty\). The direction of the ray indicates that this interval extends to positive infinity.

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