How to graph $f(x)$

Question

we have these functions :

$f(x) = \sqrt{1-\lfloor x \rfloor^2}$

$g(x) = \sqrt{\lfloor x \rfloor^2 - 1}$

How we can graph these functions ? (without using computation!)

Please Help Me !

Answer 1

You have $f(x)=1, \text{ if }0\le x <1$ and $f(x)=0, \text{ if }1\le x < 2 \text{ or } -1 \le x <0.$ For other $x$ values you will have complex roots.

IMO you cannot graph $g(x)$ without computing, because there will be function values $\sqrt{3}, \sqrt{8}$ etc.