For the argument to be valid, we must ensure that our functions are
continuous in the range in question. For example, $f(1.9) \approx
-10.9$ and $f(2.1) \approx 8.9$, but there is no zero between these
values since the function in not continuous at $x = 2$.
However $f(2.9) \approx -8.9$, and $f$ is continuous for $2 < x
< 3$ so there is a root between $2.1$ and $2.9$.