Answer: Based on the information you provided, it seems that the correct answer is "left 6 units, down 1 unit." This translation will map the graph of the function f(x) = x² onto the graph of the function g(x) = x² - 6x + 6.
To understand why this is the case, it helps to understand what the different parts of the function g(x) represent. The term x² represents the original function f(x) = x², the term -6x represents a horizontal translation of the graph of f(x) by 6 units to the left, and the constant term 6 represents a vertical translation of the graph of f(x) by 1 unit downward. Together, these transformations map the graph of f(x) onto the graph of g(x).
Note that if we were to apply the other translations you listed, they would not produce the correct graph. For example, if we were to apply a translation of "right 3 units, down 3 units," this would produce a graph that is shifted 3 units to the right and 3 units down, which is not the same as the graph of g(x). Similarly, if we were to apply a translation of "right 6 units, down 1 unit," this would produce a graph that is shifted 6 units to the right and 1 unit down, which is also not the same as the graph of g(x).