Answer
False.
Work Step by Step
Note that for decreasing values near $0$, $f(\frac{1}{10})=\frac{1}{1/10}=10$ and $f(\frac{1}{1000})=\frac{1}{1/1000}=1000$ However, for increasing values near $0$, $f(-\frac{1}{10})=\frac{1}{-1/10}=-10$ and $f(-\frac{1}{1000})=\frac{1}{-1/1000}=-1000$ Therefore, from the negative side, the function approaches $-\infty$ and from the positive side the function approaches $+\infty$. Therefore, this statement is false.
