Question

What is its domain?
What is its range?

Write the answer in interval notation.

Answer 1

Answers:

Domain = [-3, 3]

Range = [-1, 2]

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Step-by-step explanation:

The domain is the set of all allowed x inputs. Visually, the left-most point is when x = -3, so -3 is the smallest allowed x input. We have a closed circle at this endpoint, so this endpoint x value is included. In contrast, if you had an open circle, then you would exclude the endpoint.

Similarly, we have a closed endpoint at the other side as well when x = 3. This is the largest allowed x value. The domain is the set of x values such that
`-3 \le x \le 3` meaning x is between -3 and 3, including both endpoints. This translates to the interval notation of [-3, 3]. The square brackets say "include the endpoint".

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The range is the set of possible y outputs of a function. The lowest the function goes is when y = -1, and the highest is when y = 2. We include both endpoints. The range as a compound inequality is
`-1 \le y \le 2` which converts to the interval notation of [-1, 2]