On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?

The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}

Domain is all the x's and range is all the y's. There's no reason why you couldn't pop any x into the given equation and calculate it and get a number out. So literally ANY x can be used and found on this graph. So the domain is all real numbers, one of the first two answers is going to be the right one. Now, the range is all the y's on the graph. The problem says that the parabola opens down, which means it has a highest point. There is no graph above that point. That's the point (-1, 16). So 16 is the highest y-value you can find on the graph. All the rest of the y's are smaller. The range is all the y's such that the y's are 16 and smaller...in math that's written {y | y <= 16} So the second answer is the right one.

MrRoyal MrRoyal · Answer 2 · 2022-06-30T05:53:07+02:00

The domain is all real numbers. The range is {y | y ≤ 16}

How to determine the domain and the range?

The attached graph completes the question

Calculating the domain

The function is given as:

f(x) = -x² - 2x - 15

The above function is a parabola or a quadratic function.

Quadratic functions have their domain to be the set of all real numbers.

Hence, the domain is all real numbers.

Calculating the range

On the graph, we have the maximum value of y to be:

Maximum = 16

Because the parabola opens down, the range would be:

y ≤ 16

Hence, the range is {y | y ≤ 16}

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