Question

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

Answer 1

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\}`

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Step-by-step 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"