Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?
left 3 units, down 3 units
right 3 units, down 3 units
left 6 units, down 1 unit
right 6 units, down 1 unit

When you convert x^2-6x+6 into vertex form, you'll end up with (x-3)^2-3

So g(x) = (x-3)^2-3

Going from x^2 to (x-3)^2-3 means we do two things:
A) shift 3 units to the right, which is what the x-3 does
B) shift 3 units down, due to the -3 at the end

So the final answer is choice B

See the attached image for a comparison of the two graphs. Note the color coding. Also note the vertex points A and B, which are (0,0) and (3,-3) respectively. To go from point A to point B, we move 3 units to the right and 3 units down. This confirms what choice B is saying.