Below is the graph of y=3x".Translate it to make it the graph of y=3(x-4)3 +1.

There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis
Horizontal shifts:
[tex]y=(x\pm a)^n[/tex]Vertical shifts
[tex]y=x^n\pm a[/tex]Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.
Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.