2 or more Transformations

Exercises for students
Sketch the following curves on paper and check your graphs using the above applet:

y = 2 x2,	y = -2 x2,	y = (x+1)2,	y = (x-1)2,	y = x2 + 1,	y = x2 - 1
y = 2 sin(x),	y = 0.5 sin(x),	y = sin(2x),	y = sin(0.5x),	y = sin(x - 1),	y = sin(x + 1)
y = sin(x) + 1,	y = sin(x) - 1,	y = 2 sin(x) + 1,	y = 2 sin(2x) + 1
y = 1/x,	y = 1/(x-1),	y = 1/(x-1) + 1,	y = ln(x-1),	y = exp(x) - 1
y = tan(2x),	tan(3x),	tan(0.5x),	tan(x+pi/2),	tan(x-pi/2)

Summary

y = a f (bx + c) + d

As a increases, the graph is stretched by factor a parallel to the y-axis.
As b increases, the graph is compressed by factor b parallel to the x-axis.
As c increases, the graph is shifted to the left by c units.
As d increases, the graph is shifted upwards by d units.
If a is negative, the graph is reflected in the x-axis.
If b is negative, the graph is reflected in the y-axis.







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