Understanding Patterns, Relations, and Functions

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Understanding Patterns, Relations, and Functions

FUNCTIONS

Functions are a special kind of relation .

At first glance, a function looks just like a relation.

EXAMPLE:{ (0,1) , (5, 22), (11,9) }

Like a relation, a function has a domain and range made up of the x and y values of ordered pairs.

RELATIONS

A relation is just a set of ordered pairs.

Some Examples of Relations include { (0,1) , (55,22), (3,-50) } { (0, 1) , (5, 2), (-3, 9) } { (-1,7) , (1, 7), (33, 7), (32, 7) }

Note: { } are the symbol for "set"

DIFFERENCES BETWEEN RELATION AND FUNCRTION

In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value.

Geometric And Numeric Patterns

Common Number Patterns

An Arithmetic Sequence is made by adding some value each time.

Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ...

This sequence has a difference of 3 between each number. The pattern is continued by adding 3 to the last number each time.

Grades 3–5 Expectations:

represent and analyze patterns and functions, using words, tables, and graphs.

describe, extend, and make generalizations about geometric and numeric patterns;