Question

Use the graph of the function to find its domain and range. Write the domain and range in interval notation

Answer 1

Answers:

Domain:  $(-\infty, 5)$

Range:  $[-3, \infty)$

Both are in interval notation. There's a square bracket next to the -3, and everything else is a curved parenthesis.

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Explanation:

The domain is the set of allowed x input values of a function. We have a hole at x = 5, so this value is not allowed in the domain. But we can use anything smaller than this. The domain as an inequality is $x < 5$ which is the same as writing $-\infty < x < 5$ and that directly translates to the interval notation of $(-\infty, 5)$

The curved parenthesis say "exclude this endpoint". The domain is anything between negative infinity to 5, excluding both endpoints.

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The range is the set of possible y outputs of a function.

The lowest the function goes is at y = -3. The arrow indicates it goes up forever, meaning that the range as an inequality is $y \ge -3$ which is the same as $-3 \le y$ and the same as $-3 \le y < \infty$

Then that directly turns into the interval notation of $[-3, \infty)$

We have a square bracket at -3 to include this endpoint. We can't ever reach infinity, so we of course can't include this endpoint. Always use parenthesis for either infinity.