Transformation of Graphs 图的变换

This applet shows you the effect of each transformation on a graph.

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Exercises for students
Sketch the following curves on paper and check your graphs using the above applet:
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 = (x+1)2,y = (x-1)2,y = x2 + 1,y = x2 - 1
y = 1/x,y = 1/(x-1),y = exp(x-1),y = exp(x) - 1


Summary
y = a f(x)The graph is scaled by factor a parallel to the y-axis.
If a is negative, the graph is reflected in the x-axis.
y = f(ax)The graph is scaled by factor 1/a parallel to the x-axis.
If a is negative, the graph is reflected in the y-axis.
y = f(x + a)The graph is translated in the direction of the negative x-axis by a units.
If a is negative, the graph is translated in the direction of the positive x-axis.
y = f(x) + aThe graph is translated in the direction of the positive y-axis by a units.
If a is negative, the graph is translated in the direction of the negative y-axis.








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