Question

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}.

Answer 1

Domain: all real numbers. Range: {y | y ≤ 16}.

Reason: f(x) = −x^2 − 2x + 15 is a polynomial (domain = all real numbers). The parabola opens downward and has vertex at (−1, 16), the maximum y-value, so y ≤ 16. Thus the correct choice is the second option.