differential calculus question?

They mean the same thing, it's just a different way of writing it. In and after Calculus it will become more convenient to write f(x) instead of y, usually.

PSR2

It is all the same. Y is an answer. When you plug in a number (what x is) you get y (the answer). All f(x) is when you put in x into function f, this is your answer. Then they can have multiple functions.

Example:

f(x)=2x

g(x)=x+1

what is g(x) x f(x) when x is 3?

so g(x)=g(3) and f(x)=f(3)

plug it in (2x3)x(3+1)

6x4

=24

And there are many more forms and stuff you will work with this, so its key you know this.

Hope this helps.

You let y = f(x), because it allows you to graph the function on the x-y plane.

You graph by choosing a value for x, using that value to compute the value of f(x), and then assigning that value y, repeatedly to obtain a sufficient number of (x, y) pairs of points to graph the function.