A (single variable) function is a rule/method/formula/diagram/graph/etc. that produces exactly one output value for each possible input value. Inputs are usually referred to as $x$-values or simply as inputs. Outputs of functions are usually referred to as $y$-values or just the outputs of the function at given specific input values.

One can think of a function as a machine that takes certain inputs, does something to them, and returns an output. See diagram below.

Often, we often don’t even know what a function does with inputs in order to produce outputs. Sometimes, on the other hand, we are able to “look under the hood” and see exactly how the function works. All of this depends on how a function is being represented.

In the topics below, we will discuss several different ways of representing functions in a bit more depth than the video above, and also analyze what outputs are produced by the function given certain specific inputs, and vice versa.

Lesson Content

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Using Potato Diagrams

Using Sets/Lists of Ordered Pairs and Tables

Using a Given (Algebraic) Rule

Using Graphs and Plotting Them from Rules

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