It seems to me that they (on videos) keep calling the value on the y axis f(x). Why don't they just call it y?

Question

myininaya · Answer

y=f(x)
just means y is a function of x

anonymous · Answer

it is the same thing.  plugging in any arbitrary value of x in to f(x) will give you a  y-value

anonymous · Answer

okay good thanks that's what I was thinking but not sure if I was missing something in that...

anonymous · Answer

have to disagree.  
$$y=x^2$$ is not a function.  it is an equation. if you want a function you have to write it as one.  you could say "Let $$f(x)=x^2$$ or you could say let F be the set of all points $$(x,x^2)$$ or even let f be the set of points (x,y) such that 
$$y=x^2$$

anonymous · Answer

by function as opposed to equation... you mean, a function gets graphed?

anonymous · Answer

but the function is not the equation and that causes much confusion further down the line.  the function is f, not f(x).  in my previous example the function was 'the squaring function'

anonymous · Answer

the function is the action.

anonymous · Answer

once you have named your function you can talk about and say things like 
'over what interval is it increasing?" or 
'is it continuous?' or 
'is it differentiable?'

anonymous · Answer

what is true is that when you graph a function you graph 
$$y=f(x)$$ so the connection is there.

anonymous · Answer

okay, cool, so the point is to differentiate between functions and equations, that makes sense, and I can know what it is and then assume its just y... :)

anonymous · Answer

I mean, think of it as y...

anonymous · Answer

yes the notation is abused all the time so do not fret about it.  for example math teacher will say "consider the function y = 2x" which is not a function at all.  what they means is consider the function f given by all ordered pairs that satisfy y = 2x.  the "function" is just the doubling function

anonymous · Answer

so yeah, think of it as y

anonymous · Answer

thankyou :)