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Svetradugi [14.3K]
3 years ago
11

Can someone help me with number 8 please? Thank you.

Mathematics
1 answer:
Naddik [55]3 years ago
6 0
Answer: -4 \le x \le 5
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 \left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\}

------------------------------------------------------------------------------

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 -4 \le x \le 5 (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 \left\{x|x\in\mathbb{R}, \ -4\le x\le 5\right\} is the set-builder notation way of expressing the domain. The x\in\mathbb{R} portion means "x is a real number"

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