# 1 multiplication versus addition a and b are being

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(1) Multiplication versus Addition: A and B are being multiplied while C and D are being added (or subtracted). Multiplying changes the SHAPE or ORIENTATION of the graph. Such transformations are called Dilations or Reflections (respectively). Adding changes the LOCATION of the graph. Such transformations are called Translations (or Shifts). Like the rules of your Dear Aunt Sally, when sketching a new graph by a sequence of successive transformations, multiplication transformations must be done before addition transformations. If you understand the sequence of transformations, you should be able to sketch transformations in a single step without going through the transformations. (2) Inside verses Outside: B and C are on the inside of the parent function while A and D are on the outside of the function. Changes to the inside of the function affect the x- values, or the function’s inputs. This means the horizontal nature of the graph will change, either dilated, reflected, or shifted. Changes to the outside of the function will affect the y- values, or the function’s outputs. This means the vertical nature of the graph will change, either dilated, reflected, or shifted. ***As a rule of thumb, inside changes are OPPOSITE of what they immediately appear to be, while outside changes are EXACTLY as you would suspect. We will see this soon in an example, and if you’d like, I can even show you why.

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