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A constant function is a periodic function.
A. True
B. False

Answer
VerifiedVerified
501.3k+ views
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Hint: We need to check whether the given statement is true or false. A periodic function can be defined as a function returning to the same value at regular intervals. A function f is said to be periodic if, for some non-zero constant P , it satisfies the equation, f(x+P)= f(x) , for all values of x in the domain . P is the period of the function. A constant function, f(x)=c repeats its values at regular intervals.

Complete step by step answer:
We need to check whether the statement “ a constant function is a periodic function” is true or false.
Let us see what a periodic function is.
A periodic function can be defined as a function returning to the same value at regular intervals.
For example, sinx .

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The function repeats continuously in a similar fashion. For example, from the figure, the wave begins from 0 to 3 goes to the negative part from 3 to 6. This fashion is repeated again.
A function f is said to be periodic if, for some non-zero constant P , it satisfies the equation, f(x+P)= f(x) , for all values of x in the domain . P is the period of the function.
Constant function a real-valued function of a real-valued argument, denoted by f(x)=c .
The below figure shows the graph of constant function f(x)=2 .
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f(x)=2 repeats its values at regular intervals like for x=1,2,....n , where n=Z , an integer.
Hence, a constant function is a periodic function with a period n.
Hence, the given statement is True.
Note:
 All constant functions are periodic irrespective of its type, that is, whether it is an integer, a fraction, or real number. f(x+P)= f(x) is the equation of a periodic function. All constant functions repeat its values at regular intervals like for x=1,2,....n , where n=Z .
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