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

The function is a parabola which opens downwards.
-x^2 - 2x + 15
-(x^2 + 2x) + 15
= -[(x + 1)^2 - 1 ]+ 15
= -(x + 1)^2 + 16

The domain is all real numbers and the range is {y|y <= 16}
Its the second choice.