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Topic: Left Right Translation of Functions

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Subject:   RE: Left Right Translation of Functions
Author: Mathman
Date: Dec 5 2004
On Dec  4 2004, Mike Shepperd wrote:
> There is no difference in the treatment of translations (and
> dilations) between those in the x direction and those in the y
> direction. To see this clearly, consider the equation of a function
> in the form:
(y - k)/a = f((x-h)/b)

The graph of this function
> is the graph of y=f(x) subject to the following transformations:
> dilation factor b in x direction
  dilation factor a in y direction
> translation distance h in x direction
  translation distance k in y
> direction

Respectfully, Mike ... Doesn't that just state *what* happens, with following
samples, but not *why*?  That is, it states what each parameter does, but gives
no reason.  It is true that, as yo usuggest, a study of graphs reveals the
patterns, but the students need to see it in the algebra.  Since the problem the
students are having is knowing why something is moved in a positive direction
when a number is negative, isn't it more informative to show that y-a = A
becomes y = A+a, and the move is in the positive direction? Likewise, if y =
x-d, then x=y+d, and the move is again in the positive direction.
Alternately, y+a = A results in y=a-a, and a move in the negative direction
,and the same for x.  Functions unresolvable for "x" do need further
explanation, but the idea can still be shown.


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