can someone tell me if I am correct
graph y1=(1/3)^x and y2= (1/3)^x+2
the relationships between the two graphs is they are separated horizontally by 2 units
no, they are separated vertically.
y1 = y2 - 2
To separate horizontally, you need the 2nd x to be 2 less than the first.
y1 = (1/3)^x
y2 = (1/3)^(x-2)
Since the new x-values are 2 less than the old ones, it's as if the y-axis had been shifted 2 units to the right.