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Discussion: All Tools in Algebra II on Computer
Topic: Functions as objects?


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Subject:   RE: Functions as objects?
Author: stek
Date: Nov 30 2005
On Nov 29 2005, Susan wrote:
> I was wondering if there is a way to plot a function in Sketchpad,
> and then have it behave as an object.  For example, I can graph f(x)
> = sqrt (x), but I would like to make it an object so that I could
> move it freely.  I would also like to be able to reflect it over the
> x or y axis using the transformations menu.  I know that I can do
> this algebraically by writing and graphing a new function, but I was
> thinking about just being able to do it geometrically.  Any ideas?

Hi Susan,

I can give you a few answers about making functions and function plots behave
the way you want.

First, you say that you'd like to be able to move the graph of f(x) = sqrt(x)
freely. I'm not quite sure what you mean by this -- (a) do you want to move
the graph around on the screen with its coordinate system, so that the equation
stays the same, or (b) do you want to move the graph while the coordinate system
stays fixed, so that the equation changes?

If it's (a) you want, you can do it easily. You can create the graph on a
separate coordinate system (so it doesn't affect any other graphs in your
sketch) and you can hide the graph's coordinate system (so that it appears you
are dragging only the graph itself).

If it's (b) you want, this is a bit harder, because Sketchpad has no built-in
way to drag a graph and see the equation change. You can create the same effect
using two coordinate systems, one visible and one hidden. The function f(x) =
sqrt(x) should be graphed on the hidden coordinate system. You can then measure
the translation between the two coordinate systems, and display a second
equation in the form f(x) = sqrt(x - h) + k to represent the equation relative
to the visible coordinate system. Dragging the graph around will then change the
second equation. (I hope this makes sense; it feels to me more complicated to
describe than to do. If you like I'd be happy to send you a sketch that does
this.)

Second, you said you'd like to be able to reflect the graph over an axis using
geometric transformations. Though you can't directly transform function plots or
loci in this way, you can do so indirectly. Construct a point on the function
plot and transform the point however you want (for instance, by reflecting
across either axis, by reflecting across y = x, or by using dilation or
rotation). Then select both points (the one on the function plot and its
transformed image) and construct the locus.

I hope this helps.

Scott

Scott Steketee
Sketchpad Projects

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