4. periodicity

A function f is said to be periodic with a period T if, for some nonzero constant T, we have: f(x + T) = f(x) for all values of x. If there exists a least positive constant T with this property, it is called the prime period. A function with period T will repeat on intervals of length T, and these intervals are sometimes also referred to as periods.

Example: f(x) = sin x, is a periodic function and its prime period is T = 2π

sin (x + 2π) = sin x


Decide if these sentences are true or false:

a) f(x) = |x| is a periodic function

True. False.

b) f(x) = tan x has T = 2π as prime period

True. False.

c) f(x) = dec(x) is a periodic function and T = 1 is its prime period

True. False.

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