Possible wrong answer to Spivak calculus chapter on graphs of functions
Yes, it does appear to be wrong if it is the plain ‘greatest integer’ function and not something more special. The problem is where $x<0$.
Although $\frac{1}{x} \to 0 $ as $x \to -\infty$, since $\frac{1}{x} < 0$ for all $x < 0$, the lines drawn on the left hand side of a plot of $y = f(x)$ should always be at $y = -1$ or below.
The floor function $\lfloor x \rfloor$ gives the greatest integer less than or equal to $x$ and so clearly it will be $0$ only if $x \geq 0$.