Relations and Functions

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 no more than one point of the graph of a relation, then the relation is a function.

zeros

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

Arithmetic Squence

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

common difference

the difference (d) between consecutive terms in an arithmetic sequence

Arithmetic Sequence Formula

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

coordinate plane

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

x-axis

the horizontal number line in 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

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 of 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 in the range.

function

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