I am an engineer and I want to describe that a parameter depends on the value of other parameters. Is it correct if I write formally "is a function of"?
For example, the step size of a solver depends on the end time of the simulation and the relative error of solver. Could I say in a formal way $stepSize=f(rel_{err},t_{end})$? Thank you very much for your help!
Yes, you can say $stepsize$ is a function of the error and the end time.
However it might not be neccessary to introduce the name $f$ for that function. You could just write: $$stepsize = stepsize(err, t_{end})$$
However saying "stepsize is dependent on the error and the time" will probably be equally valid in most scenarios.