Find g(x), where g(x) is the translation 4 units left of f(x)=8(x–2)2+1.

To find the function g(x) which is the translation 4 units to the left of the function f(x) = 8(x–2)²+1, we need to adjust the x-values in the function by adding 4 to the x term inside the parentheses. This is because moving to the left on the graph corresponds to decreasing the x-values, which is achieved by adding to the x term in the function.

So, the function g(x) is:

g(x) = 8((x+4)–2)²+1 = 8(x+2)²+1

So, g(x) = 8(x+2)²+1 is the function that is 4 units to the left of f(x) = 8(x–2)²+1.