Function notation is using symbols to show the dependent and independent variables more clearly.
The most common symbols used for this is f(x) which is said out loud as "f of x." The symbols show that x is the independent variable and f is the dependent variable.
Function notation does not change equations, it is only a different way to show equations. This table shows how you can replace the typical y= format of and equation/graph with function notation.
Why does function notation matter?
Function notation allows mathematicians to more easily abstract functions, one example of this is to make it easier to write rules for transformations.