A periodic function is a function whose values repeat after a certain variation on the independent variable, that variation is called period.
Formally, a function f is periodic and its period is T if and only if for all values of x, the following expression is true:
If the function f is bounded between two values, the maximum M and the minimum m, then the amplitude is half the difference between those values:
To summarize, a periodic function always repeats its value after a period, which is a fixed variation of the independent variable. The amplitude is half the difference between the maximum and minimum values of the function over a period.
To find a periodic function, search for a repeating pattern (the graph of an electrocardiogram is an example of a periodic function, and the period is equal to the heart rate).
To find the period of the function, identify the horizontal distance over the x-axis where the shape of the function repeats
.Finally, to find the amplitude of a graph draw two horizontal lines tangent to the maximum and minimum values of the function and identify the vertical distance between the maximum and the minimum values. Divide that amount by 2 to find the amplitude.