The world is full of periodic phenomena.

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The world is full of periodic phenomena. The
tides come in and go out again and again, each
cycle or period lasting about 12.4 h. The amount
of daylight increases and decreases with a period
of one year. The functions that describe periodic
behavior are called periodic functions.
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Periodic functions
A function f is periodic if there is a positive
number p, called a period of f, such that
for all x in the domain of f.
The smallest period of a periodic function is
called the fundamental period of the function.
The definition of a periodic function with period
p, then is
for all x and any integer m.
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If a periodic function has a maximum value M and
a minimum value m, then the amplitude A of the
function is given by      
Example 2. Find the amplitude of the function f
described in example 1.  
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Stretching and Shrinking Graphs
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Translating Graphs
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