Final answer:
The Function Translation g(x), which is derived from the function -5|x+7|+8 being translated 3 units left, is g(x) = -5|x+10| + 8.
Step-by-step explanation:
When we talk about a function being translated, it means we are shifting the function either along the y-axis (up or down) or x-axis (left or right) without changing its shape. In this case, the function -5|x+7| + 8 is being translated 3 units to the left along the x-axis. So to find the value of the function g(x) we need to adjust the x parameter in the absolute value function by the amount of translation i.e. 3 units. Therefore, g(x) = -5|x + 7 + 3| + 8 or g(x) = -5|x+10| + 8.
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