Periodic function:
A periodic function 
must have the characteristic of 
where 
is the period.
Horizontal shift of a function:
The graph of 
is the graph of 
shifted horizontally by a units.
Vertical stretching of a function:
The graph of 
is the graph of 
stretched vertically by a units.
Horizontal shrinking of a function:
The graph of 
is the graph of 
shrunk horizontally by a units..
Reflection and vertical shift of a function:
The graph of 
is the reflection of the graph 
about x-axis.
The graph of 
is the graph of 
shifted vertically by a units.
Sinusoidal functions:
Functions whose equations satisfy 
.
Amplitude:
Amplitude is a nonnegative scalar measure of the magnitude of sinusoidal functions.
Period: For a sinusoidal function 
the absolute value of is the period of the 
sinusoidal function.
Phase shift of a sinusoidal function:
For a sinusoidal function 
the value of 
is the phase shift of the sinusoidal function.
