Combining a horizontal transformation with a vertical transeration: 6. (a) Let f be a function. Find a formula for the function whose graph is obtained from the graph of f by shifting two units to the left and then by stretching vertically by a factor of three. Then, nd the function whose graph is obtained from the graph of f by stretching vertically by a factor of three and then by shifting two units to the left. (b) George and Laura are trying to graph 2 sin(3x). Laura wants to do the horizontal compression followed by the vertical stretch, but George insists on the reverse order. Which method is correct? Why? (c) John wants to move up, and Teresa is willing to move to the left. Can they graph sin(x + %) + 1? What two graphing transformations would they use? Does the order of the transformations matter? (d) State a general principle about transformations, on the basis of parts (a), (b), and (c)