What is the equation of the graph?

Question

My Maths Mentor at first explained us the graph of the equation $y=[x]$ which looks like the following

then with a smile on the corner of this mouth he told

"It seems that you have understood the aforesaid graph.Then tell me what will be the equation of the following graph be?"

He gave us two weeks timing.I could not resist so I asked this question here I dont if this graphs are even related?

Answer 1

hint

You can treat the graph as a parametrized curve. choose a parameter $t $ and define $(x(t),y(t)) $ for $t\in [n,n+1] $ and $n\in\{-1,0,1,2,3\} $.

Answer 2

A hint: what you are looking for is the graph of the following equation, rotated $45$ degrees and dilated by a suitable constant factor:

$$y = \left|x - \lfloor x\rfloor - \frac12\right| - \frac12.$$

See what Wolfram Alpha shows for this equation.