why are function notation important?

I don't know that it is important. However, it is a convenient shorthand notation that speaks to the variables and the function rather plainly.

what do you mean speaking to the variables can you give me an example of what you refer to please.

Certainly! When we use function notation, we are able to clearly communicate what variables are involved in a certain function. For example, consider the function f(x) = x^2. The variable "x" represents an input value, and the function "f" represents the rule that takes that input value and squares it. By using the notation f(x), we are explicitly stating that the function "f" is acting on the variable "x". This notation allows us to differentiate between different variables and keep track of what role each one plays in the function. It also helps us to understand and discuss functions in a more organized and concise manner.