| A | B |
|---|
| function | from a set A to a set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. the set A is the domain (or set of inputs) of the function, and then set B contains the range (or set of outputs) |
| domain | the set of all values taken on by the independent variable x |
| range | the set of all values taken on by the dependent variable y |
| implied domain | the set of all real numbers for which the expression is defined |
| f | name of function |
| y | dependent variable |
| x | independent variable |
| vertical line test | a set of points in a plane is the graph y as a function of x if and only if no vertical line intersects the graph at more than one point |
| graph of a function | the collection of ordered pairs, [x, f(x)], such that x is in the domain of f |
| increasing | x1 < x2, f(x1) < f(x2) |
| decreasing | x1 > x2, f(x1) > f(x2) |
| constant | f(x1) = f(x2) |
| even | graph is symmetric with respect to y-axis |
| odd | graph is symmetric with respect to origin |
