How can we erase graph of $f(x)=-10a((x/a)-[x/a])$ from specific parts?

Question

The function $$f(x)=-10a(\frac{x}{a}-[\frac{x}{a}])$$ I want to erase some parts of graph from $x=a$ to $2a$ and from 3a to 4a ... And so on How can i accomplish that? I have no idea of how can we do that also please suggest any resource from which i can learn these transformation

Answer 1

You can do a piecewise-defined function:

$\forall\ \text{even } n\ge0$,

$f(x)=\begin{cases}\text{undefined}&a(n+1)<x<a(n+2)\\-10a\left(\frac xa-\left[\frac xa\right]\right)&\text{for all other values of }x\end{cases}$

Not sure if it is the right notation but I basically want $n$ to be all the even whole numbers so that $x$ is between every odd multiple of $a$ starting with $a$ to $2a$.

Also, $-10a\left(\frac xa-\left[\frac xa\right]\right)$ simplifies down to zero for $a\ne0$ just in case you didn't know.