How to determine the range of OY and OX values?

Question

Mathematics

There are different graphs of functions, but we are talking about those that have arithmetic and trigonometric functions in the set of operations.
So, suppose the user enters a formula. In this case, the graph may not cross the axes at all (for example: k / x), it can cross OX many times without crossing OY (for example: ctg (x)). Plus, offsets are added to this using constants.
How can one uniformly define the range of OY and OX without user input, as Wolfram Alpha does, for example?
I already have an application, I'm trying to set it up so that it works correctly.
It may be impossible in principle and you need to additionally parse a bunch of conditions. But something tells me there is a way.
It is impossible to stupidly measure the maximum and minimum (even if the user enters OX), because many functions quickly go to infinity, and complete game comes out.

Answer 1

I think it is possible to define presets for frequently used functions and define ranges for each specific preset.
For all functions and for complex solutions like y=six(x)+1/x+e^x^x this will not work