how do you know what to call a number after seeing what it does?

Question

eg how do you know that a value compresses or stretches an equation?
how can you tell if something vertical stretches/compresses or horizontally compresses/stretches?

Answer 1

If y = f(x)
y = f(x/k) scales horizontally by a factor of k
y/k = f(x) scales vertically by a factor of k
go to some online graphing site and play around there till this starts to make sense.