Relations and Functions

Function

A function is a relation in which each element of the domain corresponds with exactly one element in the range.

discrete graph

A graph composed of isolated points.

continuous graph

A graph is continuous if it has no jumps, breaks, or holes.

Interval notation

A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval.

set-builder notation

A notation used to describe the elements of a set.

one-to-one

A one-to-one function is a function for which each y-value in the range corresponds to exactly one x-value in the domain. A one-to-one function f has an inverse 𝘧−𝟣 that is also a function.

average rate of change

The average rate of change of the function over the interval 𝘢≤𝘹≤𝘣 is equal to 𝘧(𝘣)−𝘧(𝘢)𝘣−𝘢 .

domain

The domain of a relation is the set of all inputs, or x-coordinates, of the ordered pairs.

zero of a function

A zero of a function 𝘧(𝘹) is any value of x for which 𝘧(𝘹)=𝟢 .

relation

Any set of ordered pairs.

maximum

The maximum of a function is the greatest value that the function attains in its domain. It is the y -coordinate of the highest point on the graph of the function.

minimum

The minimum of a function is the least value that the function attains in its domain. It is the y-coordinate of the lowest point on the graph of the function.

range

The range of a relation is the set of all outputs or y-coordinates of the ordered pairs.