Translations and Compressions
Author: John Maharry
Date: 4/1/2009

An applet to use to develop intuition about compressions and translations of functions. Drag the values of a,b,c and d with the sliders to see how each changes the origininal function.

Try to match the red Shifted function to the blue Target Function.

Based on a Geogebra applet by Scott May

a - horizontal compression
b - horizontal translation
c - vertical expansion
d - vertical translation

ShiftedFunc(x)=c*Func(a*(x-b))+d

b = 0 (slider from -5 to 5, step 0.025)
d = 0.4250000000000007 (slider from -5 to 5, step 0.025)
Func(x) = cos(x - 0.13333333333333333) + 0.5 sin(2 * (x - 0.13333333333333333)) - 0.8666666666666667
c = 1 (slider from -5 to 5, step 0.025)
a = 1 (slider from -5 to 5, step 0.025)
ShiftedFunc(x) = c Func(a * (x - b)) + d
P: (0, Func(0))
P_t: (-b, ShiftedFunc(-b))
TargetFunc(x) = -1.5 Func(0.8 * (x - 3)) + 2.5