
A constant function is a periodic function.
A. True
B. False
Answer
501.3k+ views
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 is said to be periodic if, for some non-zero constant , it satisfies the equation, , for all values of in the domain . is the period of the function. A constant function, 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, .
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 is said to be periodic if, for some non-zero constant , it satisfies the equation, , for all values of in the domain . is the period of the function.
Constant function a real-valued function of a real-valued argument, denoted by .
The below figure shows the graph of constant function .
repeats its values at regular intervals like for , where , an integer.
Hence, a constant function is a periodic function with a period .
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. is the equation of a periodic function. All constant functions repeat its values at regular intervals like for , where .
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,

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
Constant function a real-valued function of a real-valued argument, denoted by
The below figure shows the graph of constant function

Hence, a constant function is a periodic function with a period
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.
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