Graph of the function $[\frac{1}{x}]$

Question

I'm interested in the graph of the function $[\frac{1}{x}]$. may seems simple, also I graphed it myself. But there is difference between my solution and the manual solution. Here is the solution of the solution manual:
But I think it's wrong about $x<-1$.
any response appreciated.

Answer 1

If by $\left[\frac{1}{x}\right]$ you mean "the integer part of $x$", then the plot is correct.

Note that if $x < -1$, then $\left|\frac{1}{x}\right| < 1$, so $\left[\frac{1}{x}\right]$ has integer part $0$.

Edit: This answer is based on the following convention: http://mathworld.wolfram.com/IntegerPart.html

Answer 2

When $x\to-\infty$ the reciprocal $1/x$ is strictly between $-1$ and $0$ and therefore the integer part (the largest integer smaller than $x$) is $-1$. The graph you reproduced shows the value $0$ for large negative $x$, which is incorrect.