Transformation of Graphs

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Summary

y = af(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) + a:
The 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.





You can define functions using these operators:
+-*/**
abs( )sqrt( )ln( )exp( )pi
sin( )cos( )tan( )
asin( )acos( )atan( )