Translation and Compressions Applet
This applet is designed to
develop intuition about translation, expansions and contractions of
functions. In particular it graphs a function named Func, and a
second function ShiftedFunc defined by
ShiftedFunc(x)=c*Func(a*x+b))+d.
The values of a, b, c, and d
are controlled by sliders. The definition of Func(x) and the view
window can be changed with the control panel.

It is worthwhile to note the transformation caused by changing the
prameters one at a time:
 Setting (a, b, c, d) = (1, 0, 1, 0) gives the original function.
 Setting (a, b, c, d) = (1, h, 1, 0) gives ShiftedFunc(x) =
Func(x+h) a horizontal translation left by h.
 Setting (a, b, c, d) = (1, 0, 1, k) gives ShiftedFunc(x) =
Func(x)+k a vertical translation up by k.
 Setting (a, b, c, d) = (m, 0, 1, 0) gives ShiftedFunc(x) =
Func(m*x) a horizontal contraction by m.
 Setting (a, b, c, d) = (1, 0, n, 0) gives ShiftedFunc(x) =
n*Func(x) a vertical expansion by n.
 Setting (a, b, c, d) = (1, 0, 1, 0) gives ShiftedFunc(x) =
Func(x) a reflection across the y axis.
 Setting (a, b, c, d) = (1, 0, 1, 0) gives ShiftedFunc(x) =
Func(x) a reflection across thex axis.
It is also wothwhile to note functions that show off transformations
clearly:
 Func(x)=abs(x) has a single corner. Translations are easy
to recognize. However a horizontal contraction by m is
indistinguishable from a vertical expansion by 1/m.
 Func(x)=x^2 has a single vertex. Translations are easy to
recognize. However a horizontal contraction by m is
indistinguishable
from a vertical expansion by 1/m^2.
 Func(x)=sqrt(1x^2) graphs as a half cicle. Almost all
transformations are easy to
recognize. The only problem is that a reflection across the y
axis gives back the same graph.
Created
with GeoGebra.
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The home for the applications is
http://www.geogebra.org.
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Last updated By Mike May, S.J.,
September 23, 2007.