Algebra Trigonometry - Polynomial and Rational Functions

Learn Polynomial and Rational Function and How to Work with Them
Rating: 4.4 out of 5 (50 ratings)
8,889 students
Algebra Trigonometry - Polynomial and Rational Functions
Rating: 4.4 out of 5 (50 ratings)
8,889 students
Understand and work with rational functions. They can also use the course in a series planned by Great IT Courses to learn math all the way up to calculus.

Requirements

  • You need to have a computer connected to the Internet to watch the lectures.
  • Ideally, you need to have taken the course prior to this: Algebra and Trigonometry - Linear Functions which can be found on Udemy.
Description

This course teaches you all the important underlying concepts in Polynomial and Rational functions in mathematics. The knowledge that you gain here can be further completed in our next courses towards a complete mastery of calculus.

This course covers the following topics: 

  • Quadratic Functions
  • Power Functions and Polynomial Functions
  • Graphs of Polynomial Functions
  • Dividing Polynomials
  • Zeros of Polynomial Functions
  • Rational Functions
  • Inverse and Radical Functions
  • Modeling Using Variation

This course has been taken from chapter 5 of the book, "Algebra Trigonometry" from openstax, ISBN-10: 1-947172-10-7. The book can be downloaded free of cost from their website. All chapters of the book have been planned to be produced as a video course by us. This course contains around 175 videos each averaging 15 minutes. Using this course, you'll learn polynomial and rational functions from scratch really well. 

Also, this course can be taken as part of a series that will take you all the way up to mastering calculus. All the courses in the series will be taken from the same book described above and other calculus books from openstax. You can read our "Mathematics" page on "GreatITCourses" website to make yourself more familiar with our road map. A Google search will take you to our website.  

Who this course is for:
  • Anyone who wants to learn polynomial and rational functions.
Curriculum
9 sections177 lectures28h 23m total length
  • Instructor Introduction
  • Course Curriculum
  • Road Map
  • How to Best Use This course
  • Feedback
  • Legal Disclaimer
  • Course and Section Introduction
  • Recognizing Characteristics of Parabolas
  • Identifying the Characteristics of a Parabola - Example
  • Parabola Graphs and their formulas - Part 1
  • Parabola Graphs and their formulas - Part 2
  • Writing the Equation of a Quadratic Function From a Graph
  • Finding the Vertex of a Quadratic Function - Solution 1
  • Finding the Vertex of a Quadratic Function - Solution 2
  • Writing a Quadratic Equation in Standard and General Form - Solution 1
  • Writing a Quadratic Equation in Standard and General Form - Solution 2
  • Finding the Domain and Range of Quadratic Functions - Part 1
  • Finding the Domain and Range of Quadratic Functions - Part 2
  • Finding the Domain and Range of a Quadratic Function - Example
  • Finding the Domain and Range of a Quadratic Function - Example
  • Determining the Minimum and Maximum of a Quadratic Function
  • Finding the Maximum Value of a Quadratic Function - Example
  • Finding Maximum Revenue - Example - Part 1
  • Finding Maximum Revenue - Example - Part 2
  • Finding the x and y-intercepts of a Quadratic Function
  • How to Factorize a Quadratic Function
  • Finding the x-intercepts of a Parabola
  • Finding the x and y-intercepts of a Quadratic Function - Example
  • Applying the x-intercept and Vertex of a Parabola - Example
  • Power Functions and Polynomial Functions - Introduction
  • Identifying Power Functions
  • Identifying End Behavior of Power Functions - Part 1
  • Identifying End Behavior of Power Functions - Part 2
  • Identifying the End Behavior of a Power Function - Example
  • Identifying Polynomial Functions
  • Identifying Polynomial Functions - Example
  • Identifying the Degree and Leading Coefficient of a Polynomial Function
  • Identifying the Degree and Leading Coefficient of a Polynomial Function -Example
  • Identifying End Behavior of Polynomials - Part 1
  • Identifying End Behavior of Polynomials - Part 2
  • Identifying End Behavior and Degree of a Polynomial Function - Example
  • Identifying End Behavior and Degree of a Polynomial Function - Example
  • Identifying End Behavior and Degree of a Polynomial Function - Example
  • Identifying Local Behavior of Polynomial Functions
  • Determine the Intercepts of a Polynomial Function - Example
  • Determining the Intercepts of a Polynomial Function With Factoring - Example
  • Determining the Intercepts of a Polynomial Function - Example
  • Comparing Smooth and Continuous Graphs
  • Number of Intercepts and Turning Points - Example
  • Drawing Conclusions about a Polynomial from the Graph - Example
  • Drawing Conclusions about a Polynomial from the Factors - Example
  • Drawing Conclusions about a Polynomial from the Factors - Example
  • Graphs of Polynomial Functions - Introduction
  • Characteristics of Graphs of Polynomial Functions
  • Recognizing Polynomial Functions - Example
  • Using Factoring to Find Zeros of Polynomial Functions
  • Finding the x-intercepts of a Polynomial Function by Factoring - Example
  • Finding the x-intercepts of a Polynomial Function by Factoring - Example
  • Finding the y and x-intercepts of a Polynomial in Factored Form - Example
  • Finding the x-intercepts of a Polynomial Function Using a Graph - Example
  • Finding the x-intercepts of a Polynomial Function Using a Graph - Example
  • Identifying Zeros and Their Multiplicities
  • Identifying Zeros and Their Multiplicities - Example
  • Determining the End Behavior of Polynomial Functions
  • Relationship Between Degree and Turning Points in Polynomials
  • Finding the Maximum Number of Turning Points of a Polynomial
  • Graphing Polynomial Functions
  • Sketching the Graph of a Polynomial Function - Example
  • Sketching the Graph of a Polynomial Function - Example
  • Intermediate Value Theorem
  • Using the Intermediate Value Theorem - Example
  • Using the Intermediate Value Theorem - Example
  • Writing Formulas for Polynomial Functions
  • Writing a Formula for a Polynomial Function from the Graph - Example
  • Writing a Formula for a Polynomial Function from the Graph - Example
  • Local and Global Extrema of Polynomial Functions
  • Using Local Extrema to Solve Applications - Example
  • Dividing Polynomials
  • Long Division Algorithm Modeling
  • Comparing Long Division Model with a Long Division Example
  • Dividing Two Polynomials Using Long Division Algorithm
  • Division Algorithm - Formal Statement
  • Polynomial Long Division - Example
  • Polynomial Long Division - Example
  • Polynomial Long Division - Example
  • Using Synthetic Division to Divide Polynomials
  • Using Synthetic Division to Divide Polynomials - Example
  • Using Synthetic Division to Divide Polynomials - Example
  • Using Synthetic Division to Divide Polynomials - Example
  • Using Polynomial Division to Solve Application Problems
  • Using Synthetic Division to Divide Polynomials - Example
  • Section 5.5 Introduction
  • Remainder Theorem
  • Remainder Theorem - Example
  • Remainder Theorem - Example
  • Factor Theorem
  • Factor Theorem - Example
  • Factor Theorem - Example
  • Rational Zero Theorem - Part 1
  • Rational Zero Theorem - Part 2
  • Rational Zero Theorem - Example
  • Rational Zero Theorem - Example
  • Rational Zero Theorem - Example
  • Finding the Zeros of Polynomial Functions
  • Fundamental Theorem of Algebra
  • Fundamental Theorem of Algebra - Example
  • Linear Factorization Theorem
  • Linear Factorization Theorem - Example
  • Linear Factorization Theorem - Example
  • Descartes' Rule of Signs
  • Descartes' Rule of Signs - Example
  • Descartes' Rule of Signs - Example
  • Solving Real-World Applications - Part 1
  • Solving Real-World Applications - Part 2
  • Rational Functions Introduction
  • Arrow Notation
  • Local Behavior of a Function
  • End Behavior of a Function
  • Using Arrow Notation - Example
  • Using Arrow Notation - Example - Part 1
  • Using Arrow Notation - Example - Part 2
  • Using Transformations to Graph a Rational Function - Example
  • Transformations, Graph, Vertical and Horizontal Asymptotes - Example - Part 1
  • Transformations, Graph, Vertical and Horizontal Asymptotes - Example - Part 2
  • Solving Applied Problems Involving Rational Functions
  • Domains of Rational Functions
  • Identifying Vertical Asymptotes of Rational Functions
  • Identifying Vertical Asymptotes - Example
  • Finding Removable Discontinuities in the Graph of Functions
  • Identifying Horizontal Asymptotes of Rational Functions - Part 1
  • Identifying Horizontal Asymptotes of Rational Functions - Part 2
  • Identifying Horizontal Asymptotes of Rational Functions - Part 3
  • Identifying Horizontal and Slant Asymptotes - Example
  • Identifying Horizontal Asymptotes - Example
  • Identifying Horizontal and Vertical Asymptotes - Example
  • Intercepts of Rational Functions
  • Finding the Intercepts of a Rational Function - Example
  • Finding x and y-intercepts, horizontal vertical asymptotes - Example - Part 1
  • Finding x and y-intercepts, horizontal vertical asymptotes - Example - Part 2
  • Finding x and y-intercepts, horizontal vertical asymptotes - Example - Part 3
  • Graphing Rational Functions - Part 1
  • Graphing Rational Functions - Part 2
  • Graphing a Rational Function - Example - Part 1
  • Graphing a Rational Function - Example - Part 2
  • Writing the Equation of Rational Functions
  • Writing the Equation of Rational Functions - Example
  • Inverse Functions Introduction
  • Graphical Relationship Between Inverse Functions
  • Inverse Function Definition
  • Why Study Inverse Functions
  • Finding Inverse of Quadratic Functions - Part 1
  • Finding Inverse of Quadratic Functions - Part 2
  • Finding Inverse of Quadratic Functions - Part 3
  • Finding Inverse of Quadratic Functions
  • Inverse Functions Characteristics
  • Verifying Inverse Functions
  • Verifying Inverse Functions
  • Finding the Inverse of Cubic Functions
  • Finding the Inverse of Cubic Functions
  • Restricting the Domain to Find the Inverse of a Polynomial Function - Part 1
  • Restricting the Domain to Find the Inverse of a Polynomial Function - Part 2
  • Finding the Inverse of a Radical Function
  • Finding the Inverse of a Radical Function
  • Solving Applications of Radical Functions
  • Section 6 (Previous Section) Review - Part 1
  • Section 6 (Previous Section) Review - Part 2
  • Section 6 (Previous Section) Review - Part 3
  • Domain of a Radical Function composed with a Rational Function - Part 1
  • Domain of a Radical Function composed with a Rational Function - Part 2
  • Finding Inverse of Rational Functions
  • Finding Inverse of Rational Functions
  • Solving Direct Variation Problems
  • Solving Inverse Variation Problems
  • Solving Inverse Variation Problems - Example
  • Solving Inverse Variation Problems - Example
  • Solving Joint Variation Problems
  • Solving Joint Variation Problems - Example

Instructor
Mathematics
Great IT Courses
  • 3.9 Instructor Rating
  • 342 Reviews
  • 22,121 Students
  • 17 Courses

At Great IT Courses, you can follow a simple but effective system to learn mathematics. By following our road map, you'll be taken through all the ups and downs of mathematics starting from the basics (class 6) all the way through calculus (class 12).

Wherever you get stuck, we will assist you so that you can keep moving and finish the road map.

With us, you will learn how to reason your way through mathematics logically and not just memorize some formulas.