Question

If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?

Answer 1

y = |x - 4|

Explanation:

Because the x value is the only variable that changed, it means the graph has moved only horizontally. The only value you are adding to will be inside the absolute value, not outside (as that is vertical transformation)

If that is the case, the graph has only moved right from (1, 1) to (4, 1), and thus from the parent graph y = |x| you would derive y = |x - 4|.