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Introduction
Many of our conjectures involve a rule or formula, perhaps in terms of a general integer \(n\text{.}\) We can represent such rules formally using the concept of a function and function notation. A function describes a relationship between variables, often thought of as the input (or independent variable) and the output (dependent variable).
In algebra or calculus, the input and output of functions are usually real numbers. Those are one kind of function, but functions can have any type of input and output values, including discrete objects such as integers, strings, and sets, graphs.
We begin this chapter in Section 6.1 with the definition of a function and some examples of functions defined by formulas. Many functions in mathematics, computer science, data science, and business are defined in words, which is the topic of Section 6.2. We look at key properties of functions in Section 6.3 and Section 6.4 including one-to-one, onto, composition, and inverses. Finally, in Section 6.5 we look at sequences (infinite lists) which are a type of function.
