Free DictionaryLinks to an external site. defines relation as a logical or natural association between two or more things; relevance of one to another; connection. When we think of relationships, we think of how two things are associated. Some relationships we consider to be good and some we may consider to be bad; but, either way, we are describing how two or more things interact or get along with each other. This is the same in mathematics. A relation is considered to be the correspondence, or association, between two sets. Some relations are super special; we call these functions. Functions are the basis of algebraic concepts. We will spend this module learning what it means for a relation to be a function. We'll look at the ways that functions can be represented and how to determine if a graph, set of ordered pairs, or equation has the qualities of a function. Functions have special characteristics. We will explore a couple of these in this unit, and you will learn more and more of these characteristics as you progress through your mathematical career. Finally, in our module, we'll pay particular attention to rate of change, or slope, and how to determine if a function is increasing or decreasing and on what interval that is occurring.
Essential Questions
What is the definition of a function?
How do we know if a graph represents a function?
What are some of the different ways functions can be represented?
How can we compare the properties of functions that are represented in different ways?
Key Terms
The following key terms will help you understand the content in this module.
Domain - Domain of a relation is the set of all x-coordinates of the ordered pairs of that relation.
Function - A rule of matching elements of two sets of numbers in which an input value from the first set has only one output value in the second set.
Graph of a Function - The set of all the points on a coordinate plane whose coordinates makes the rule of function true.
Range of a Function - The set of all output values or the y-values of a function or a relation is called the range of the function or the relation.IMAGE SOURCE: CLIPART.COM
F - Functions Note Taking Guide F - Functions: Relation and Representation Lesson
Functions Module OverviewFree Dictionary Links to an external site. defines relation as a logical or natural association between two or more things; relevance of one to another; connection. When we think of relationships, we think of how two things are associated. Some relationships we consider to be good and some we may consider to be bad; but, either way, we are describing how two or more things interact or get along with each other. This is the same in mathematics. A relation is considered to be the correspondence, or association, between two sets. Some relations are super special; we call these functions. Functions are the basis of algebraic concepts. We will spend this module learning what it means for a relation to be a function. We'll look at the ways that functions can be represented and how to determine if a graph, set of ordered pairs, or equation has the qualities of a function. Functions have special characteristics. We will explore a couple of these in this unit, and you will learn more and more of these characteristics as you progress through your mathematical career. Finally, in our module, we'll pay particular attention to rate of change, or slope, and how to determine if a function is increasing or decreasing and on what interval that is occurring.