PLEASE I BEG ANYONE WHO SEES THIS QUESTION TO PLEASE HELP ME TO PLEASE GIVING A CORRECT ANSWERS OR CHOICES PLEASE I'LL GIVE 50 POINTS Hi I really need help with this problem please.

Correct answers only

the choices are:

equal to

1 greater than

1 less than

2 greater than

2 less than

3 greater than

3 less than

The maximum value of g(x) is 3 greater than the maximum value of f(x).

Step-by-step explanation:

The function modeled by the equation, f(x) = - (x - 3)² + 9, represents a quadratic function in vertex form.  

The vertex form is given by: f(x) = a(x - h)² + k, where:

⇒ The value of a is the vertical compression or stretch factor, which essentially determines the width of a parabola. The value of a also determines where the graph of a parabola opens:

⇒ (h, k) = Vertex of the parabola.

Given these definitions, we can assume the following information regarding  the quadratic function,  f(x) = - (x - 3)² + 9:

The vertex form of an absolute value function is given by: g(x) = a|x - h| + k, where:  

⇒ The value of a determines the following:

⇒ (h, k) = Vertex of the absolute value function.

⇒ x = h represents the axis of symmetry.

The axis of symmetry is the imaginary point on the graph that intersects through the h-coordinate of the vertex, thereby dividing the graph into two symmetrical parts.

Observing the given table of values, especially how the y-values increasingly peak towards g(x) = 12, then decreases back down starting at g(x) = 8.  It is important to take notice of the y-values, as it represents the resulting output provided by the given input (x-value).  

The increasing, followed by the decreasing y-values imply that the graph must be facing downward. Since we specified that the maximum point provided by g(x) = 12, then it means that it is the vertex occurs at point, (1, 12).

Therefore, the maximum value of g(x) is 3 greater than the maximum value of f(x).  

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step-by-step explanation: