Final answer:
The graph of the absolute value function that is vertically stretched by a factor of 2, then shifted 3 units left and 8 units down, is represented by the equation f(x) = 2|x+3|-8, which is Option A.
Step-by-step explanation:
The student is asking which equation represents the graph of the absolute value parent function that has been vertically stretched, then shifted 3 units to the left and 8 units down. The transformations applied to the parent function |x| are a vertical stretch by a factor of k, a horizontal shift to the left by h units, and a vertical shift down by v units. This results in the general form of f(x) = a|x-h| - v, where a represents the vertical stretch, h the horizontal shift, and v the vertical shift.
To determine which equation correctly represents the function with these transformations, we need to apply the rules for shifting and stretching. A vertical stretch by a factor of 2 would transform the parent function into 2|x|. Shifting this function 3 units to the left requires replacing x with x+3, resulting in 2|x+3|. Finally, shifting 8 units down is represented by subtracting 8 from the function, giving 2|x+3|-8. Therefore, the correct equation that represents this transformed function is Option A: f(x) = 2|x+3|-8.