I am reviewing my maths and came across definition of a function. According to it, for each input(x) it needs to have corresponding output(y). This one - f(x) = (x-3)/(x-3) - doesn't have y for x=3. The same for y=sqrt(x) or y=5x^2 + x^1/4 - first one doesn't have y for x<0 and the second one for x>0 has two values.
Despite of this they(or similar expressions) are called in some books or videos as 'functions'.
My question is does it matter if they are formally called functions or not if we actually can do with them all the things we do with functions?
I would appreciate if someone could explain it to me