4.1 Functions
A function is one of the concepts in math that sounds pretty abstract but is really straightforward once you get experience with it. Thought of in terms of numbers, a function takes a value and returns one and only one value.
For example, for any real number, we can square it. That process is a function. For any non-negative real number, if we take the positive square root of it then we get another function. If we were to say we got both the positive and negative square roots, we would not have a function.
We use the notation f(x) for a function, meaning that we start with some value x, do something to it indicated by the definition of f, and the result is f(x). The f can be any letter or word, but we use f because the word ‘‘function’’ starts with it and we are not being especially creative. It’s common to see g and h but, really, we can use anything.
We write a function definition like f(x) = x2 or g(x) = √x...