The concept of a function as a mathematical machine, the notation f(x)=…, and function tables / diagrams.
Want a deeper conceptual understanding? Try our interactive lesson!
No exercises available for this concept.
Practice exam-style functions and their properties problems
A function is a mathematical machine that produces exactly one output for each input it is given.
A function can be evaluated for specific values of x by plugging the value into the expression of the function.
A function diagram shows how a set of inputs is mapped to a set of outputs with arrows pointing from inputs to outputs.
Powered by Desmos
Multiple arrows can point to the same output, but each input must have exactly one arrow, since a function always gives the same output for a given input.
The inputs and outputs of a function can be represented in a table where one row shows inputs, and the other shows outputs:
To find f(some value), look for that value in the first row, then look at the row below it. For example, f(11)=2.