Relations and Functions Defintions

Coordinate Plane

Formed by the intersection of two number lines, the horizontal axis and the vertical axis.

x-axis

The horizontal axis on a coordinate plane.

y-axis

The vertical axis on a coordinate plane.

Quadrants

The four regions into which the x- and y-axis separate the coordinate plane.

Origin

The point at which the x- and y-axis intersect on the coordinate plane; (0,0).

Ordered Pair

A set of numbers, or coordinates written in the form (x,y)

x-coordinate

The x-value of an ordered pair, represents the horizontal placement of the point.

y-coordinate

The y-value of an ordered pair, represents the vertical placement of the point.

Discrete Graph

A graph that consists of points that are not connected

Continuous Graph

A function graphed with a line or smooth curve.

Relation

A set of ordered pairs.

Domain

The set of first numbers (x-values) of the ordered pairs in a relation.

Range

The set of second numbers (y-values) of the ordered pairs in a relation.

Mapping

Illustrates how each element of the domain is paired with an element of the range.

Function

A relation in which each element of the domain is paired with exactly one element of the range.

Function Notation

A way to name a function that is defined by an equation. Replace “y” with “f(x)”.

Input

A value substituted for an x-value in a function.

Output

The result of substituting a value into a function.

Vertical Line Test

If any vertical line passes through the graph of a relation no more than once, then it is a function.

Zeros

The x-intercepts of the graph of a function. The points for which f(x)=0

Arithmetic Sequence

A numerical pattern that increases or decreases at a constant rate/value.

Common Difference

The difference between consecutive terms in an arithmetic sequence.

Arithmetic Sequence Formula

A formula used to find the nth-term of an arithmetic sequence.