Is there any way to shift distance between zeroes of function $-10(x-[x])$ by $a$ units on x axis?

Question

The function is $$-10(x-[x])$$ Now i wonder if we can shift distance between zeroes of this function by a units is it possible? I tried replacing x with x-1 but it doesn't work

Answer 1

The function is periodic with period $1$, so when you replace $x$ with $x-a$, and $a$ is any whole number, the graph will look the same as the unshifted graph (because you are shifting by a multiple of the period). Try letting $a$ be something other than a whole number.

EDIT: To add on about why $f(\frac{x}{a})$ changes the period from $1$ to $a$.

We know the period of $f(x)$ is $1$, which tells us $f(x+1)=f(x)$ for all $x$ in the domain. The same is true for any function with period $1$.

Let $g(x)=f(\frac{x}{a})$. We can see that $g(x+a)=f(\frac{x+a}{a})=f(\frac xa+1)=f(\frac xa)=g(x)$.

That line of reasoning should also show that there is no number $b$, where $0<b<a$, such that $g(x+b)=g(x)$, so $a$ is the period for $f(\frac xa)$.