Intervals

Functions: Domain and range

Intervals

IntervalAn interval is a collection of numbers that correspond with a part of the numbers line. We identify the following intervals.

Interval	Description	Image
#\ivoo{a}{b}#	#x \gt a \land x \lt b#
#\ivcc{a}{b}#	#x \geq a \land x \leq b#
#\ivco{a}{b}#	#x \geq a \land x \lt b#
#\ivoc{a}{b}#	#x \gt a \land x \leq b#
#\ivoo{a}{\infty}#	#x \gt a#
#\ivco{a}{\infty}#	#x \geq a#
#\ivoo{-\infty}{b}#	#x \lt b#
#\ivoc{-\infty}{b}#	#x \leq b#
#\ivoo{-\infty}{\infty}#	all numbers

Write down the interval #\ivco{-3}{-1}# with inequality signs, in which #x# is up front at each inequality. If there's more than one inequality, connect them through #\land#.

#x \geq -3 \land x \lt -1#

The interval #\ivco{-3}{-1}# describes all numbers bigger than or equal to #-3# and smaller than #-1#. Hence, we notate this as
\[x \geq -3 \land x \lt -1\]

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