What is a function in mathematics?
Q: What is a function in mathematics?
A: A function in mathematics is an object that produces an output when given an input, which could be a number, vector or anything that can exist inside a set of things.
Q: What are the two sets associated with functions?
A: The set of all values that x can have is called the domain and the set that contains every value y can have is called the codomain.
Q: How are functions often denoted?
A: Functions are often denoted by italic letters such as f, g, h.
Q: How do we represent a function?
A: We represent a function by writing y = f(x), where f is the name of the function and one writes f : X → Y (function from X to Y) to represent the three parts of the function - domain (X), codomain (Y) and pairing process (the arrow).
Q: Can you give an example of a function?
A: An example of a function is f(x) = x + 1. One gives a natural number x as input and gets natural number y which is x + 1. For example, giving 3 as input to f results in an output of 4.
Q: Does every function need to be an equation?
A: No, not every function needs to be an equation. The main idea behind functions is that inputs and outputs are paired up somehow - even if it might be very complicated.
