3.4: (a, b)
In this section, both endpoints are not included in the interval.
\((2,5)\)
Solution
The interval above includes all numbers between 2 and 5, but because the interval has parentheses on both the left and the right sides of the interval, the end points are not included.
\((-4,10)\)
Solution
Similar to the explanation for the previous examples, the end points are not included in the interval. So the interval includes every number between -4 and 10, but not -4 and 10.
By now, students should have a strong idea of the numbers that are included and not included in the examples above. Students should also be able to analyze any given number line and write the appropriate interval notation for that number line. Try the following exercises to check for understanding.
Draw a number line for the following intervals and list at least three numbers inside the set.
- \((0,1)\)
- \((-11,-5)\)
- \((100,325)\)
- \((5,6)\)
- \((12.1, 26.55]\)
Draw a number line that corresponds to the following intervals.
- \([-2,3)\)
- \([-5,-2]\)
- \((0,5]\)
- \((-3,4)\)
- \([-3,-2]\)
- \((-7,2.5)\)
Write the appropriate interval notation for the given number lines.