Given that (-9,-1) is on the graph of f(x) find the corresponding point for the function f(x+3).

If you begin with the graph for f(x) and then substitutde x+3 for x, the effect on the graph will be to move the whole graph 3 units to the left.  

Given that (-9,-1) is on the graph of f(x), and that we are to move the entire graph 3 units to the left, then the coordinate -9 becomes -9-3, or -12:  (-12,-1).