I am wondering what the importance of function notation is? And why is it:confused: ?

Please explain what you want to know.

Function notation, e.g. f(x), simply tells us that this is a function of x.

y = f(x)

This means that for some specified values of x, there are corresponding values of y.

The function simply signifies a correspondence between values of x and y.

Note the f(x) does not have to be an algebraic expression like x^3.

The following also defines a function y = f(x).

{When x = 1, y = 2;
When x = 7, y = 5;
When x = 9, y = 0}

This establishes correspondence between certain values of x (1, 7, 9) and values of y
(2, 5, 0)

The essence of a "function" is such "correspondence".

Similarly, the following establishes a correspondence and defines a function:

y = x when x > 0; y = x + 5 when x <= 0.

Note that there should be only one value of y corresponding to each value x.