We can sort transformations of graphs into two types -x
transformations or y transformations. Anything else is a combination
of an x transformation followed by a y transformation or vice versa.
A transformation is an x transformation if it is an
argument of a function on the right hand side, or if it can be
written in brackets without looking like nonsense. For instance,
these are some x transformations:
x transformations are always counter – intuitive..To
transformyou
might think you scale by 2 in the x direction. THIS IS WRONG!!! You
scale byYour
graph becomes compressed in the x – direction, not expanded. And to
transformyou
do not subtract 2 from all the x's, hence moving the graph left. You
add 2 to all the s's and move the graph right.
Y transformations are easier.implies
correctly, a scaling by 2 in the y direction. Notice the difference
between sin2x or sin(2x) which is an x transformation and 2sinx ,
which is a y transformation. These are some more examples of y
transformations:
y transformations are always intuitive. To
transformyou
move the graph up 1, and forwe
scale by 4 in the y direction.
Sometimes we can have a combination of transformations:
represents
a scaling by 3 in the y direction FOLLOWED by a movement up 2. It
would be wrong to do it the other way round.
represents
a scaling of 3 in the y direction and a scaling byin
the x direction. This is illustrated above.
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