I need some help to confirm my answer is correct.

Let $x$ be a real number.

Let $f(x):=x-\lfloor x\rfloor$. That is, $f(x)$ is the fractional part of $x$.

If $b-a=1$,
what is the image of $f$ on $[a,b]$?

Is the image $[0,1)$? 

Thanks!!