Question

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}.

Answer 1

Answer:b

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

we have

$f(x)=-x^{2}-2x+15$

This is a the equation of a vertical parabola open downward

The vertex is a maximum

The vertex is the point (-1,16)

see the attached figure

therefore

The domain of the function is all real numbers ----> interval (-∞,∞)

Te range of the function is

$y\leq 16$

All real numbers less than or equal to 16 ----> interval  (-∞,16]