3.3: (a, b]

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Victoria Dominguez, Cristian Martinez, & Sanaa Saykali
Citrus College via ASCCC Open Educational Resources Initiative

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Be careful with how the interval notation is written! The notation in this section looks similar to the previous section, but they are not same. By looking at the notation closer it becomes clear that the endpoint on the left is not included in the set while the endpoint on the right is included in the interval.

Example 3.3.1

\((2,5]\)

Solution

The left endpoint, which corresponds to number 2 is not on the interval. The right endpoint, which corresponds to number 5 is included. Examples of numbers in this set is 3, 4, 4.5 and 5

Example 3.3.2

\((-4,10]\)

Solution

The endpoints of this interval behave the same way as example 1. When graphing, remember to place \(\bullet\) when endpoint is included and \(\circ\) when the endpoint is not included. Some examples of numbers in this interval are -3.99, -2, 0 and 10.

Exercise 3.3.1

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

\((6,12]\)
\((-31,-20]\)
\((-200,-199]\)
\(\left(\dfrac{3 }{4} ,5 \right] \)
\(\left(\dfrac{−11 }{2} , \dfrac{7 }{2} \right]\)
\((0.15, 6.95]\)