Martin was drawing these line segments (see the picture) and was explaining to his friends: “When you draw identical line segments like this, in the same direction to the right and left, you get a graph of a periodic function.”
His friends recalled discussing this property of a function in school but could not agree on the period.
Michael said that the period is the number $3$ and demonstrated his statement in the picture:
Eric claimed the period to be the number $4$ and also demonstrated his statement in the picture:
David tried to persuade his friends that the period is the number $\sqrt{34}$ and demonstrated his statement in the picture:
Peter was convinced that the period is the number $23$ and also demonstrated his statement in the picture:
Which boy has NOT made a mistake?
Eric
Michael
David
Peter
Function $f$ is periodic if and only if there is a real number $P>0$ such that the following conditions hold simultaneously:
1) For all $x$ in the domain, the number $x\ +kP$, for any $k\in\mathbf{Z}$, also belongs to the domain of the function.
2) For all $x$ in the domain, holds $f\left(x\right)=f\left(x+kP\right)$ for any $k\in\mathbf{Z}$.
The number $P$ is called the period of the function. In our case, both conditions are fulfilled only by the number $4$.
