Mathematicians, transcendental is a very broad word. Why isn't there a narrow word just for exponential and logarithmic? Transcendental is compared to algebraic, but there is no hyponym of transcendental to denote exclusive set of exponential and logarithmic.
For almost all of software development exponential, logarithmic, and linear time functions are highly relevant, but rarely are other transcendental functions like trigonometric and hyperbolic relevant unless in niche lines of work. When training junior developers, I always emphasize the importance of exponential and logarithmic, but mathematics has provided no succinct word to denote their importance.
More detail:
As mathematical exponential functions are the inverse of logarithmic functions, I would expect this special relationship be signified by a specific mathematical word.
Consider other logical supersets. For example, "transput" is the hypernym of "input" and "output". "Computerware" is the hypernym of "hardware" and "software".
"Transcendental" is an overshoot for the hypernym of "exponential" and "logarithmic". Yes, where I typically employ the word is in the context of time complexity, but I anticipate that set/category theory of mathematics has previously prescribed a solution.
What is niche about trigonometric and hyperbolic functions? Don't you have students who want to program games or flight simulators or GPS applications or ...?
The functions that I think your students are really interested in are called elementary functions. These functions are the ones that are supported by as library functions in most programming languages and that feature in the most important applications in economics, physics, engineering and ... That's why they are implemented as library functions and that's one of the reasons why they have been given a collective name in pure mathematics.
Note: if you are mainly interested in functions relevant for use as complexity measures, then it doesn't do much harm to talk about the elementary functions as throwing in trigonometric functions and hyperbolic functions doesn't add anything new from the complexity measure point of view: a function with time complexity $|\sin|$ operates in constant time, while a function with time complexity $\sinh$ operates in exponential time.