I really just want to find the way of describing this that won’t net me comments like yours. It is very disheartening to spend so much time on something, and really try to do the topic justice, to be met with a torrent of “this is wrong, that’s wrong, this is also wrong.” Please remember I am a human being trying to do my best.
For example: "the function x^2 is O(x^3)" is a valid sentence in big-O notation, and is true.
Big O is commonly used in other places besides analysis of algorithms, such as when truncating the higher-order terms in a Taylor series approximation.
Another example is in statistics and learning theory, where we see claims like "if we fit the model with N samples from the population, then the expected error is O(1/sqrt(N))." Notice the word expected - this is an average-case, not worst-case, analysis.
In computer science f(x) is often some complexity function, like number of some specific operations when running an algorithm to completion.
Otherwise, we cannot say that 1 is O(x), for example.