Before we understand what is the Period of a graph we must know that functions can be either periodic or aperiodic (not periodic). So, a function domain can also be used to represent the period of any function. We would see same behavior of the function after completion of one period. Trigonometric functions are better examples to understand the Periodic Functions because these functions repeat their behavior after a certain interval or period. If we consider the aperiodic functions, they do not possess any periods.
To find the period of graph of any function we continuously try to analyze the graph to get 2 maxima points. These points may represent the lowermost or uppermost value or points of the same values.
Suppose we have following function:
H (x) = -4 cos 10 x and G (x) = 4 sin (8 x),
In 1st and the 2nd functions we see that functions are in trigonometric form and period for both sine and cosine functions lie between 0 to 2 pi. So, period of respective functions can be evaluated as follows:
10 x = 0 to 10 x = 2 pi,
Or period for H (x) is 0 to pi /5,
Similarly, for G (x) we can write:
8 x = 0 to 8 x = 2 pi,
Or period of G (x) is 0 to pi /4.