# Re: vertical/horizontal stretch/shrink

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Posted by Jack on September 30, 2002 at 18:52:43:

In Reply to: vertical/horizontal stretch/shrink posted by Michael on September 30, 2002 at 15:01:05:

: Hi. Since I've been looking at this I've realized our Pre Calc. class is going pretty slow. But that's okay because I've been having a lot of trouble. In one of the lessons we're working on now we are talking about shifting, reflecting, and stretching graphs. I am having major trouble distinguishing between whether it's horizontal or vertical, and whether it's a strech or shrink. Maybe I'm just not grasping the very basics here but if someone could help explain this to me I would be much, much appreciative.

:Given a function y=f(x)
:VERTICAL SHIFTING - The graph of f(x)+k is the same graph as f(x) shifted vertically. The shift is up if k>0, and down if k<0.

:HORIZONTAL SHIFTING - The graph of f(x+h) is the same graph as f(x) shifted horizontally. The shift is to the right if h>0, to the left if h<0.

:VERTICAL STRETCHING & COMPRESSION - The graph of y=af(x), a>1, is the same graph of y=f(x) stretched with respect to the y-axis by a factor a. The graph of y=f(x)/a, a>1, is the same graph of y=f(x) compressed with respect to the y-axis by a factor 1/a.

:HORZONTAL STRETCHING & COMPRESSION - The graph of y=f(ax), a>1, is the same graph of y=f(x) compressed with respect to the x=axis by a factor of a. The graph of y=f(x/a), a>1, is the same graph of y=f(x) stretched with respect to the x-axis by a factor 1/a.

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