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? 

The graph of the function is symmetric about the $y$-axis, so we only need to think about the lower bound when $x\geq 0$. And $y$ is increasing for $x\geq 0$. So the minimum occurs when $x=0$, so the greatest lower bound is $-\dfrac{3}{7}$.
