Question

The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?

Answer 1

First, you can simplify the function finding the perfect square:

$f(x)=-x^2-2x+15=-(x^2+2x)+15=-(x^2+2x+1-1)+15=-((x+1)^2-1)+15=-(x+1)^2+1+15=-(x+1)^2+16.$

This form of function gives you the coordinates of parabola vertex - (-1,16).

From the diagram you can see that all values for x are possible, then the domain is $x\in (-\infty,\infty)$ (all real numbers). Also you can see that values of y decrease from y=16 to $-\infty$, then the range is $y\in(-\infty,16]$ (or {y|y ≤ 16}).

Answer: correct choice is B.

Answer 2

Since the function is a parabola and there are no discontinuities, the domain is all real numbers. To determine the range, the function has to be transformed into the vertex form.
The vertex form of the function is:
f(x) = -(x+1)2 +16
This means that the graph is facing downwards with the vertex at (-1,16).
So, the range is {y|y ≤ 16}