I need help with this, ASAP.

Question

Function 1 is: f(x) =3^x, with points (0,1) and (1,3). Function 2 is g(x) = 3^(x-3)-1. Find how many units was function 2 translated horizontally, how many units it was translated vertically, and an equation for the horizontal asymptotic of the graph of g.

Answer 1

That's a good question. Using my TI-83 calculator, I find that Function 2 is translated three units to the right (because of x - 3 instead of only x) and one unit down (because 1 is subtracted from the y values).

As for the horizontal asymptote of Function 2, for large negative values of x, 3^(x - 3) approaches zero, meaning the function approaches g(very large negative number) = 0 - 1. So the asymptote is y = -1.