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.

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07-06-2018
Mathematics

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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.

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cerverusdante cerverusdante · Answer 1 · 2018-06-07T01:22:56+02:00

From our graph we can infer that the our function intercept the x-axis at the points [tex](-6,0) [/tex] and [tex](-2,0)[/tex]. 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 [tex]x[/tex] where [tex]x \leq -6[/tex] or [tex]x \geq -2[/tex], and the function is negative for all real values of [tex]x[/tex] where [tex]-6\ \textless \ x\ \textless \ -2[/tex]

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