Answer: [tex]-4 \le x \le 5[/tex]
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write [tex]\left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\}[/tex]
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Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got [tex]-4 \le x \le 5[/tex] (x is between -4 and 5; inclusive of both endpoints)
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing [tex]\left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\}[/tex] is the set-builder notation way of expressing the domain. The [tex]x\in\mathbb{R}[/tex] portion means "x is a real number"
