Investigating whether a function is bounded I have the following function:
$$y=\frac{x^{2}-3}{x^{2}+7}$$
and I'm trying to determine, whether the function is bounded or not. To find the upper bound, I rewrote the function as $y=\frac{x^{2}-7+10}{x^{2}+7}$, and it's obvious that upper bound is 1. 
However, how would I find the lower bound? 

We have
$$y=\frac{x^{2}-3}{x^{2}+7}=1-\frac{10}{x^{2}+7}\ge 1-\frac{10}7$$
