Basics of Functions and Their Graphs

Satisfactory Essays
Topics: Function
1.2 Basics of Functions and Their Graphs
Introduction to Relations
Domain and Range of a Relation
Any set of ordered pairs (x,y) is called a relation in x and y. Furthermore,
The set of first components in the ordered pairs is called the domain of the relation. The set of second components in the ordered pairs is called the range of the relation.
Definition of Function and Vertical Line Test
Definition of a Function
Given a relation in x and y, we say “y is a function of x” if for every element x in the domain, there corresponds exactly one element y in the range.
Examples
Determine if the relation is a function.
1. {(8,1),(9,10),(-6,14), (0,1)}
We are looking to make sure that every element in the domain (x) is only paired with one element in the domain.
8 is paired with only 1
9 is paired with only 10
-6 is paired with only 14
0 is paired with only 1
This relation is a function because for every element in the domain there corresponds exactly one element in the range.
2. {(6,3), (14,-3), (5,7),(14,1),(8,-12)}
This relation is NOT a function because the element 14 is paired with both -3 and
1.
Vertical Line Test
Consider a relation defined by a set of points (x,y) in a rectangular coordinate system. The graph defines y as a function of x if no vertical line intersects the graph in more than one point.
Examples
1. This relation is a function because it passes the vertical line test. The vertical line only intersects the graph at one point. It doesn’t matter where the vertical line is placed for this to be true.
2. This relation is NOT a function because the vertical line intersects the graph in more than one point.
Determining Whether an Equation Represents a Function
We have seen that not every set of ordered pairs defines a function. Similarly, not all equations with the variables x and y define a function. If an equation is solved for y and more than one value of y can be obtained for a given x, then the equation does not

You May Also Find These Documents Helpful

  • Better Essays

    Graphs and Function

    • 1033 Words
    • 5 Pages

    Graphs and Function What is the relation between the graphs and function and how was it applied in the real world? Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The…

    • 1033 Words
    • 5 Pages
    Better Essays
  • Satisfactory Essays

    CHAPTER 4 : FUNCTIONS AND THEIR GRAPHS 4.1 Definition of Function A function from one set X to another set Y is a rule that assigns each element in X to one element in Y. 4.1.1 Notation If f denotes a function from X to Y, we write 4.1.2 Domain and range X is known as the domain of f and Y the range of f. (Note that domain and range are sets.) 4.1.3 Object and image If and , then x and y are known respectively as the objects and images of f. We can write , , . We can represent…

    • 643 Words
    • 5 Pages
    Satisfactory Essays
  • Powerful Essays

    Basic Functions of Os

    • 1245 Words
    • 5 Pages

    Thus the basic functions of an OS are – 1. Process Management – Managing the programs that are running. 2. Memory Management – Managing and rationing the memory between processes and data. 3. Storage Management – Managing the permanent Storage of data on disks or other media 4. I/O Management – Managing the input and output 5. Device / Resource Management – Managing devices and resources and allowing the users to share the resources 6. Security and Protection – Securing the…

    • 1245 Words
    • 5 Pages
    Powerful Essays
  • Satisfactory Essays

    Week 1 Assignment 2 DQ1: This week we were introduced to the basic functions of our computers. The three things I learned are: 1. I’ve always known that our computers come preloaded with the operating system, although I didn’t know that the Microsoft applications I have on my computer are compatible on a MAC. For example, MS word, MS PowerPoint, and MS Excel. 2. One of the things I found important to share with others was the use of external storage devices. I learned the hard way my senior…

    • 524 Words
    • 3 Pages
    Satisfactory Essays
  • Satisfactory Essays

    leaders are students of human personalities, motivation and communication. They can influence their personnel to view situations from their perspectives. Leading also involves supervision of employees and their work. Controlling Controlling is a function of management that involves measuring achievement against established objectives and goals. It also requires managers to be able to identify sources of deviation from successful accomplishment and to provide a corrective course of action. Managers…

    • 397 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    This pack includes MAT 116 Assignment Functions and their Graphs Resource: Appendix E, MyMathLab® Due Date: Day 7 [Individual forum and MyMathLab®] Complete Appendix E to apply the skills learned in Ch. 7 to a real-life situation. Use Equation Editor to write mathematical expressions and equations in Appendix E. Complete the Week Six Assignment: Ch. 7 Quiz in MyMathLab®. This assignment assesses content learned in Ch. 7. Mathematics - General Mathematics Find…

    • 617 Words
    • 4 Pages
    Satisfactory Essays
  • Better Essays

    4 Basic Functions of Management Tynesha Sutton American Intercontinental University Abstract This paper will explain the importance of the four business functions which are planning, organizing, directing, and controlling. Planning is the process of creating the business vision; Organizing is arranging the internal structure of the organization. Directing is leading the organization through proper leadership and motivation. These principles are a great model for…

    • 796 Words
    • 4 Pages
    Better Essays
  • Good Essays

    Graphs

    • 630 Words
    • 3 Pages

    Graphs are often used to deliver a visual and compelling case in many applications and businesses. Graphs are the information delivery vehicle of choice for many numerical data applications. With graphs a lot of information can be condensed into a visually descriptive object. They reduce the amount of time that would have been expended in reading or parsing through a lot of information. On the other hand, they can also be easily used to misrepresent or skew interpretation towards a favorable…

    • 630 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    Graphs

    • 686 Words
    • 3 Pages

    his budget will go to his foods with 45% of his total allowance. Next is for lodging with 30% followed by the projects and fare which will have 10%. The least designation for his budget will be for his savings which has 5% only. 2. BAR GRAPH The bar graph shows the yearly tourist count for the provinces of region V. the province of Albay got the highest number of tourist with 450 000. It is followed by the provinces of Camarines Sur and Camarines Norte with 400 000 and 350 000 respectively.…

    • 686 Words
    • 3 Pages
    Satisfactory Essays
  • Good Essays

    List and explain the four basic functions of management and provide an example of how a manager would use each function in their work. In order to be a good and effective manager one must possess four basic characteristics. He or she must be able to plan, be organized, have good leadership skills, and have control of their work environment. Management is explained by Robbins & Coulter (2007), as someone who coordinates and oversees the work activities of others so that their activities are…

    • 642 Words
    • 3 Pages
    Good Essays