When you derive a function from another using the transformation
[tex]g(x) = f(x+k)[/tex]
you're translating the graph of the parent function f(x) horizontally.
More specifically, you translate the graph k units to the left if k is positive, k units to the right if k in negative.
So, starting from the graph of f(x), you have that the graph of
[tex]g(x) = f(x+3)[/tex]
is the same graph of f(x), but shifted 3 units to the left.
