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]The graph of the function f(x) = –(x 6)(x 2) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0). 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.



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semsee45

Answer:

A)  The function is increasing for all real values of x where x < -4.

Step-by-step explanation:

The graph of the quadratic function f(x) = -(x + 6)(x + 2) is attached.

It is a downward-opening parabola that intersects the x-axis at (-6, 0) and (-2, 0), with its maximum (vertex) at (-4, 4).

A function is increasing when its slope is positive, meaning that as x increases, y also increases. Therefore, the interval over which the graphed function is increasing is x < -4.

A function is decreasing when its slope is negative, meaning that as x increases, y decreases. Therefore, the interval over which the graphed function is increasing is x > -4.

Therefore, the true statement is:

[tex]\large\boxed{\textsf{The function is increasing for all real values of $x$ where $x < -4$.}}[/tex]

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