Question

The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true? 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 < x < –2. The function is positive for all real values of x where x < –6 or x > –3. The function is negative for all real values of x where x < –2.

Answer 1

From our graph we can infer that the our function intercept the x-axis at the points
`(-6,0)` and
`(-2,0)`. Notice that bellow those two points our function is negative, whereas above those two points our function is positive. In other words: the function is positive for all real values of
`x` where
`x \leq -6` or
`x \geq -2`, and the function is negative for all real values of
`x` where
`-6\ \textless \ x\ \textless \ -2`

We can conclude that the correct answer is: The function is negative for all real values of x where –6 < x < –2.