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) = x^2? ?
show your work and explain if possible.
everything so much in : )

 The required function rule for g(x) is

Step-by-step explanation:  Given that the graph of g(x)  is f(x) translated to the left 8 units and up 2 units, where f(x) is given by

We are to find the function rule for g(x).

We know that

if a function y=p(x) is translated h units left and k units up, then h is added to x and k is subtracted from y.

For the given function, we have

h = 8 and k = 2.

Therefore, we get from (i) that

The graphs of f(x) and g(x) are shown in the attached figure below.

Thus, the required function rule for g(x) is