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Transformating Graphs of Functions

We can sort transformations of graphs into two types -xtransformations or y transformations. Anything else is a combinationof an x transformation followed by a y transformation or vice versa.

A transformation is an x transformation if it is anargument of a function on the right hand side, or if it can bewritten in brackets without looking like nonsense. For instance,these are some x transformations:

x transformations are always counter – intuitive..Totransformyoumight think you scale by 2 in the x direction. THIS IS WRONG!!! Youscale byYourgraph becomes compressed in the x – direction, not expanded. And totransformyoudo not subtract 2 from all the x's, hence moving the graph left. Youadd 2 to all the s's and move the graph right.

Y transformations are easier.impliescorrectly, a scaling by 2 in the y direction. Notice the differencebetween sin2x or sin(2x) which is an x transformation and 2sinx ,which is a y transformation. These are some more examples of ytransformations:

y transformations are always intuitive. Totransformyoumove the graph up 1, and forwescale by 4 in the y direction.

Sometimes we can have a combination of transformations:

representsa scaling by 3 in the y direction FOLLOWED by a movement up 2. Itwould be wrong to do it the other way round.

representsa scaling of 3 in the y direction and a scaling byinthe x direction. This is illustrated above.

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