3.1: [a, b]

This section will focus on intervals in the form [ , ]. By observation, the interval begins and ends with brackets. The use of brackets implies that the endpoints are being included in the set. This section will include the endpoint on the right and the endpoint on the left since again the interval notation starts and ends with brackets.

Example 3.1.1

\([2,5]\)

Solution

Figure 3.1.1

In this example , the set includes the endpoints 2 and 5, the set also includes every number between 2 and 5. Hence, 3, 3.25, 4, 4.9999, and 5 are all part of the set. When graphing the set in the number line closed bullets • are used in the endpoints that are included in the set.

Example 3.1.1

\([-4,10]\)

Solution

Figure 3.1.2

Similar to the previous example, the endpoints -4 and 10 are included in the set. The set contains all numbers between -4 and 10. Hence, the numbers -2, 0, 1, 2, 3, 4.5, 10 are some examples of numbers inside the interval \([-4,10]\).

Exercise 3.1.1

Draw a number line for the following intervals and list at least three numbers inside the set.

1. \([-3,3]\)
2. \([-23,-20]\)
3. \([-101,242]\)
4. \([2.5,3]\)
5. \([0,12]\)
6. \([-4.2,6.1]\)