Express the interval in set-builder notation and graph the interval in.docx

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The document discusses expressing an interval in set-builder notation and graphing it on a number line. The specific interval given is (-9,-1]. It provides the solution that in set-builder notation the interval is represented as {x | x > -9 and x ≤ -1} and when graphed on a number line it is shown as a line from -10 to 0 with an open circle at -9 and a closed circle at -1.

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Express the interval in set-builder notation and graph the interval in a number line.
(-9,-1]
The solution set in set-builder notation is ?
(please show your work)
Solution
When drawing this on a number line, you create a line starting at -10 and going to 0, just to show
the points past the actual interval. Then, you create a hollow circle the point at -9 and draw a line
all the way to -1 where you put a filled in circle. This means that -9 is not in your interval, but
any number above it is up until -1 which is included in your interval. In set-builder notation it is
{x | x > -9 and x <(or equal to) -1}

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