(Mathematical) Relation(ship) A link between two or more pieces of information or data. Specifically a ’relation’ (aka relationship) need not involve variables, although often the pieces of information or data in a relation are eventually generalized into variables.

Mathematical Expression A statement that involves variables and/or constants and some relationship between them. A mathematical expression does not contain the symbol ‘ \(=\) ’.

Equation Mathematical expressions or relations that involve two or more variables and an equality. That is to say, an equation is when two mathematical expressions are equal to one another.

Domain Valid input values for the independent variables of an equation.

Codomain The set (or type) of values a dependent variable can possibly have. Note that the dependent variable may not actually attain all the values of the codomain.
For example; a dependent variable may belong to the codomain of “all real numbers”, but if it is a distance, then it would have to be a positive number. See the lecture notes for an explanation of “codomain” versus “range”.

Function A specific type of mathematical relationship that relates independent and dependent variables, and yields precisely one value for each dependent variable, for any fixed combination of specific values for the independent variable(s). That is: An equation that has one “output value” for a given set of “input values”. Note: A function must have a Domain and a Codomain as part of it’s definition.

Range Output values the dependent variable actually attains, for a given function and domain pair.

Solution An answer that depends on the question asked.
Note: There is no such thing as a “universal solution to a function”.

(Functional) Argument The content that a function is being applied to.
For Example: The ”\(x\)” in ”\(f(x)\)” or the ”\(2x+1\)” in the ”\(g(2x+1)\)” are both examples of ‘functional arguments’.

(Functional) Output (or Value) The value of the codomain that a function returns or “outputs”.
For Example: If \(f(x) = 3x+1\) and we compute \(f(5) = 3\cdot 5 + 1 = 16\), then the \(16\) is an example of the ‘functional output’ (also referred to as the functions value).