Horizontal and vertical transformations are independent, meaning that it doesn’t matter whether horizontal or vertical transformations are done first. Also, the function f (b(x − h)) first does a horizontal stretch to f (x) by a factor of 1 b , then a horizontal shift by h. Similarly, af (x)+k first does a vertical stretch by a factor of a, then a vertical shift of k. From the graph of y = x2, plot the graph −(2(x − 3))2 + 4 two ways: First by doing the horizontal transformations, graphing the result, then doing the vertical transformations to the graph, graphing the new graph, second by doing the vertical transformations, graphing the result, then doing the horizontal transformations to the graph, graphing the new graph.

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Both methods are graphed and we can see that the f... View the full answer