The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?

g(x) = f(x+8)+2 = (x+8)^2 + 2

To find the function rule for g(x) given f(x) = x², we need to apply the translation described in the question.

First, let's start with f(x) = x².

To move the graph of f(x) to the left by 8 units, we need to subtract 8 from the x-coordinate of every point on the graph.

So, to translate f(x) to the left by 8 units, we can write the new function as g(x) = (x - 8)².

Next, we need to move the graph of g(x) upward by 2 units. To do this, we add 2 to the y-coordinate of every point on the graph.

Therefore, the final function rule for g(x) is g(x) = (x - 8)² + 2.

This means that g(x) is equal to f(x) translated to the left by 8 units and upward by 2 units.