# Bisection method guessing interval

I know that generally the bisection method is used given a certain function and an interval where we know a root exists within it. What if we don't know the interval? Is there a way of "guessing" the interval to use?

But let's focus now on the domain on which the function is continuous. If it's odd, then taking a huge numerical range will be fine: bisection takes only $\log_2 (max-min)$ to reduce the interval so it won't take long. However, the biggest problem here is if the function has many zeroes and it's hard to find an interval with opposite signs of the function (to bracket the zero). Random sampling could work as a last resort - sample the domain according to some distribution (even distributions that reach to infinity) and find a pair of values where the function has opposite signs.