Question

The graph of the function f(x) = –(x + 6)(x + 2) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < –4. The function is increasing for all real values of x where –6 < x < –2. The function is decreasing for all real values of x where x < –6 and where x > –2. The function is decreasing for all real values of x where x < –4.

Answer 1

From the attached graph, we see that
f(x) is increassing in (- &infin; , -4), and
f(x) is decreasing in ( -4, &#8734; )
therefore
The function is increasing for all real values of x where x < –4.   TRUE 
The function is increasing for all real values of x where –6 < x < –2.   (FALSE, f(x) is positive in this range)
The function is decreasing for all real values of x where x < –6 and where x > –2.   (FALSE,  f(x) is negative in this range)
The function is decreasing for all real values of x where x < –4.  (FALSE, f(x) is decreasing ∀ x>-4