Find g(x), where g(x) is the translation 4 units left and 2 units down of f(x)=–3(x+2)2+6.

To find g(x), we need to apply the transformations to the function f(x) = -3(x+2)^2 + 6.

1. Translation 4 units to the left: This means we replace every x in the function with (x+4). So, f(x) becomes f(x+4) = -3((x+4)+2)^2 + 6 = -3(x+6)^2 + 6.

2. Translation 2 units down: This means we subtract 2 from the entire function. So, f(x+4) becomes g(x) = -3(x+6)^2 + 6 - 2 = -3(x+6)^2 + 4.

So, the function g(x) which is the translation 4 units left and 2 units down of f(x) is g(x) = -3(x+6)^2 + 4.