On many old HP calculators, there were f and g buttons that would change the function of the key pressed. The f key was yellow and the g key was blue. What did f and g stand for?
They accessed secondary and tertiary options for other buttons, similar to the Fn key on a keyboard.
I understand that. It just seems like f and g should stand for something. F could be function. G could be???
The HP-45 only had an f key, and it was certainly “function”. My HP-25 had f and g keys. The HP-67 had f, g and h. (yellow, blue and black.)
I suppose it could have just been the next letters available given that ABCDE had been assigned for programming. And then made lowercase to distinguish them from the programming keys. This would be logical given the h key on @Francis_Vaughan‘s 67.
Until the HP-65 the handheld calculators were not programmable, So the ABCDE keys came after f, but along with g. Perhaps more interesting is that the HP-65 had a yellow f^{-1} key. Something that makes the intent pretty clear.
Going through the images on the wiki HP page and sorting by year:
HP-35 No button for alternative functions
HP-45 Unlabeled yellow button for alternative functions
HP-80 Same as 45
HP-65 f, f-1, and g. These labels coincided with ABCDE.
In mathematics texts, the usual letter used for a function is f, which of course stands for “function”. And if it’s relevant to have more than one function, further ones are called g and h, simply because those are the next letters.
I suspect that it’s the same here. And yes, it might seem unsatisfying to have one letter stand for a word, but another analogous letter to just be a letter without standing for anything. But language is often illogical.
In case you’re curious, a handful of other nerds had a similar conversation 10+ years ago 
https://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv021.cgi?read=234293
Yes, this. And I believe in more than mathematics texts. For example if you are trying to describe a function of a function, you’d symbolize it f(g(x)).
Well, yes, but if you’re abstractly discussing composition of functions, you probably are writing a mathematics text.
(if you’re describing it in a concrete context, then the functions probably have some real-world meaning, and are represented by letters corresponding to that real-world meaning)
Ask an electrical engineer what the symbol for the square root of minus one is…*
*(it’s j, of course. i stands for current)
I had totally forgotten it didn’t have an f on it. So yes, ABCDE plus f and g all came at the same time.
These calculator came from the golden age of HP and their calculator products, one where serious thought was put into everything. There was almost certainly some care put into the exact form all these keys had, and avoiding confusion. Adding an F or G key to the programming keys would have been frowned upon, But they probably felt there was a lucky coincidence that use of the letters worked out so well.
However, just to mix things a little, the HP-21 had an unlabeled blue key for accessing additional functions. So the colour moved about a bit.
But before the handhelds were the desktop machines. The 9800 series. The 9815 seems to be the first use of the yellow key, and it also had had a grey f^{-1} key. Since the machine supported the full alphabet, and shoe horned all the letters onto keys, they seem to have been very wary of having both an f and an F. Which does support the idea that even on the HP-65 they would have tried to avoid it.
I agree with the others that the “g” was used just because it’s the next letter after “f.” And that was used because it stands for “function.”
My first HP calculator was the 41C, which just had a yellow function key without a letter. And my 41C, which I bought in 1981, still works.
wow, im old enough grandpa had an old adding machine that looked like a small cash register and printed everything out like one and then dad had one of the first digital calculators that looked like a checkbook and the numbers looked like a speak and spell … and cost about 75.00 then by the late 80s you could get big solar calcs at k-mart for like 10 bucks (my fingers were too big for the ones the schools used for math class so mo bought me one …)
It does, though. f stands for function, g stands for function…
Yet an HP-15C still cost $135.
Well, I never needed one that was that technical lol I only needed one because my math teachers thought letting me do the math on a calculator might help me remember how to do it … that and I checked my own work because no one could read my writing let alone my numbers
Made me remember that while lots of computer keyboards did, and still do, have a bunch of modifier keys, the old Symbolics keyboard had spelled-out names for all of them: TOP, GREEK/FRONT, SHIFT, HYPER, SUPER, META, and CTRL. (OK, “CTRL” is abbreviated. Why?? I have at least one laptop keyboard where the “Fn” and “Alt” keys are small enough so that the abbreviations are understandable, but the nice and big control key also says “Ctrl”, and the shift key has nothing but an up-arrow on it—especially confusing since there are regular arrow keys— and if they are trying to evoke a vintage typewriter or something, well, a Remington 12 distinctly says “SHIFT KEY”)
on my onn (a Walmart house brand) keyboard it says “shift” with an up arrow next to it …i wondered why the arrow…