Unit 6- Relations, Functions and Sequences

Relation

a set of ordered pairs

Functions

a relation in which no two ordered pairs have the same x-values. Each x-value is paired with only one y-value.

Vertical Line Test

A method that can quickly tell when a relation is presented on a graph, if it’s a function or not. If each vertical line drawn through the graph of a relation intersects the graph at one and only one point, then the relation is a function.

Domain

Listing all of the x-coordinates as a set.

Range

Listing all of the y-coordinates as a set.

Discrete Function

A finite set of points, write numbers from least to greatest and if a number repeats, only write it once.

Continuous Function

An infinite set of points, use an inequality or interval

Interval of Increase

The function values increase as the input values increase (left to right)

Intervals of Decrease

The function values decrease as the input values decrease (up and down)

Function Notation

f(x) is used instead of y to denote the dependent variable, it indicates that the relationship is a function, simplifies evaluation when given specific values of the independent variable.

“Zero” of a function

the x-intercept of the graph. The value of x when y=0.

Arithmetic Sequence

A list of number in which the difference between any 2 consecutive terms is constant

Common difference

The numerical difference (“d”) between any two consecutive terms.

Arithmetic Sequence

The nth term of an arithmetic sequence can be found using the following formula; an=a1+d(n-1)

a1

The first term of the sequence

Geometric Sequence

A list of numbers in which a common ratio exists between each term.

Geometric Sequence explicit formula

an=a1 x r^n-1