Spivak Calculus, Ch 4 Graphs, Problem 17v: is the solution manual solution correct? [duplicate]

In problem #17-v of Spivak's Calculus (3rd edition, chapter 4) the reader is asked to draw the graph of the function $f(x)= [1/x]$, where $[\ldotp]$ is the greatest integer function. I did the problem and then checked the answer, but the answer provided in the manual seems to be wrong. I have attached a link to the image of the answer provided in the manual: https://imgur.com/a/jN4LW4H.

Is the answer wrong?

Solution 1:

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 $x \geq 0$.