Question

Find the domain and range of all 4 problems?

Answer 1

Problem 1

The domain is $(-\infty, \infty)$ which is the same as saying $-\infty < x < \infty$ to indicate "the set of all real numbers". This is because the graph stretches on forever in both left/right directions due to the arrows at each endpoint.

Answer:

Domain = $(-\infty, \infty)$

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Problem 2

The range is $[-2, \infty)$ which is the same as writing $-2 \le y < \infty$ aka $-2 \le y$ aka $y \ge -2$.

The lowest y can go is y = -2 as shown by the vertex point. We can have y = -2 or larger. Note the square bracket next to the -2 in $[-2, \infty)$ which means we include -2 as part of the interval.

Answers:

Range = $[-2, \infty)$

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Problem 3

This time we don't have arrows at the endpoints. Rather, we have filled in circles or closed endpoints.

The smallest x can be is x = -5 as shown by the left-most endpoint.

The largest x can get is x = 5 as shown by the right-most endpoint.

The allowed interval for all possible x inputs is $-5 \le x \le 5$ which condenses into the interval notation [-5, 5]. Use square brackets to include each endpoint.

Answer:

Domain = [-5, 5]

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Problem 4

The range is the set of y values spanning from the lowest/smallest y value of y = -3 to the largest y = 3, which leads to $-3 \le y \le 3$ and further to [-3, 3]. We include both endpoints.

Answer:

Range = [-3, 3]