# Do you know its property ?-8

Algebra Level 5

Which of the following functions are periodic?

$\large a. ~~~\text{sgn}\left(e^{-x}\right)$

$\large b.~~~|\sin x| +\sin x$

$\large c.~~~\min(4\cos x,|x|)$

$\large d.~~~\left\lfloor x+\dfrac{1}{2}\right\rfloor +\left\lfloor x-\dfrac{1}{2}\right\rfloor +2\lfloor -x\rfloor$

Details and Assumptions:

• $\lfloor\cdot\rfloor$ represents the Floor Function.

• $\text{sgn}(x)$ represents the sign function. We have $\text{sgn}(x)=-1,0,1$ for negative, zero, positive $x$ respectively.

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