Discussion:  All Topics 
Topic:  Left Right Translation of Functions 
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Subject:  RE: Left Right Translation of Functions 
Author:  Mike Shepperd 
Date:  Dec 6 2004 
use of a "why through pattern" approach, especially when linked to the use of
technology.
By omitting the word "symmetry" in my original email, I may have failed to
establish clearly a "why argument". The symmetry of the form (y  k)/a =
f((xh)/b) demonstrates that the dilation factor a and translation distance k
in the y direction have their counterparts b and h in the x direction.
In my experience, students have little trouble in understanding the
transformations in the y direction but they often need help with the
transformations in the x direction.
For Windows users, download Winplot if you have not already discovered this
great freeware from Rick Parris. Enter the equation y=asin((xh)/b)+k and
create sliders for the values of a,b,h,k. Enjoy!
http://math.exeter.edu/rparris/winplot.html
On Dec 5 2004, Mathman wrote:
> 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((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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