Discussion:  All Topics in Algebra II 
Topic:  Left Right Translation of Functions 
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Subject:  RE: Left Right Translation of Functions 
Author:  Mathman 
Date:  Dec 5 2004 
> 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((xh)/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 ya = A
becomes y = A+a, and the move is in the positive direction? Likewise, if y =
xd, then x=y+d, and the move is again in the positive direction.
Alternately, y+a = A results in y=aa, 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.
David.
 
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