Question

Which statement about the function is true?

The graph of the function f(x) = (x + 2)(x + 6) is shown
below.
The function is positive for all real values of x where
x>-4.
The function is negative for all real values of x where
-6 The function is positive for all real values of x where
X<-6 orx > -3.
The function is negative for all real values of x where
x < -2.
+
4
+2
+
246
x
4+
--6-

Answer 1

The function is negative for all real values of x where -6< x < -2

Explanation:

Given f(x) = (x + 2)(x + 6)

The graph of the function is as shown in the attached figure.

As shown, we can deduce the following:

The function is positive for all real values of x where x > -2 and x < -6

The function is zero at x = -2 and x = -6

The function is negative for all real values of x where -6 < x <-2

Compare the observations to the given statements:

So, The true statement is The function is negative for all real values of x where -6 < x <-2