Pre-Calculus: Functions

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Opleiderscore: starstarstarstar_borderstar_border 6,3 Coursera heeft een gemiddelde beoordeling van 6,3 (uit 4 ervaringen)

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Beschrijving

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About this course: This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic pr…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic properties

Created by:  University of California, Irvine
  • Taught by:  Dr. Sarah Eichhorn, Associate Dean, Distance Learning & Tenured Lecturer

  • Taught by:  Dr. Rachel Cohen Lehman

Level Intermediate Language English, Subtitles: Hindi How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what learners said 課程作業

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Syllabus


WEEK 1


Course Overview and Algebra Review
We begin with an overview of the course and an opportunity to review and practice some of the prerequisite algebra skills needed for success in this course.


11 videos, 3 readings expand


  1. 閱讀: Syllabus
  2. 閱讀: Quiz Notation
  3. Video: Introduction to Algebra and Geometry
  4. 閱讀: Algebra Review: Readings and Exercises
  5. Video: Properties of Integer Exponents
  6. Video: Adding and Subtracting Polynomials
  7. Video: Multiplication of Binomials
  8. Video: Multiplication of Polynomials
  9. Video: Multiple Operations with Polynomials
  10. Video: Rational Exponents
  11. Video: Simplified Radical Form
  12. Video: Square Root Addition and Subtraction
  13. Video: Multiplication Involving Square Roots
  14. Video: Rationalizing a Denominator


WEEK 2


Linear Equations and Inequalities. Absolute Value Equations and Inequalities.
In this module, we will learn to solve linear and absolute value equations and inequalities. We will also explore a range of story problems which can be solved utilizing linear equations.


13 videos, 3 readings expand


  1. 閱讀: Linear Equations and Inequalities I: Reading and Exercises
  2. Video: Solving Linear Equations
  3. Video: Algebraic Symbol Manipulation
  4. Video: Linear Word Problems
  5. Video: Percentage Word Problems
  6. Video: Area and Perimeter Word Problems
  7. 閱讀: Linear Equations and Inequalities II: Readings and Exercises
  8. Video: Distance-Rate-Time
  9. Video: Mixture Problems Using Linear Equations
  10. Video: Solving a Linear Inequality
  11. Video: Compound Inequalities
  12. Video: Linear Inequality Word Problems
  13. 閱讀: Absolute Value Equations and Inequalities: Readings and Exercises
  14. Video: Absolute Value Equations
  15. Video: Absolute Value Inequalities
  16. Video: Inequalities Involving Radicals

Graded: Linear Equations and Inequalities I
Graded: Linear Equations and Inequalities II
Graded: Absolute Value Equations and Inequalities

WEEK 3


Quadratic Equations.
In this module, we explore a variety of methods for solving quadratic equations.


9 videos, 1 reading expand


  1. 閱讀: Quadratic Equations: Readings and Exercises
  2. Video: Introduction to Polynomials and Rational Functions
  3. Video: Factoring a Quadratic Expression
  4. Video: Special Factoring Formulas
  5. Video: Factoring by Grouping
  6. Video: Solving a Quadratic Equation
  7. Video: Discriminant
  8. Video: Quadratic Formula
  9. Video: Solving a Quadratic Equation - Completing the Square
  10. Video: Quadratic Equation Word Problems

Graded: Quadratic Equations I
Graded: Quadratic Equations II

WEEK 4


Rational and Radical Equations.
We begin this module by practicing manipulations of rational expressions using basic properties. We then utilize these manipulations to solve rational and radical equations.


10 videos, 1 reading expand


  1. 閱讀: Rational Expressions: Readings and Exercises
  2. Video: Simplifying Fractions
  3. Video: Simplifying a Ratio of Polynomials
  4. Video: Adding and Subtracting Rational Expressions
  5. Video: Multiplying Rational Expressions
  6. Video: Dividing Rational Expressions
  7. Video: Square Root Property
  8. Video: Solving Rational Equations, Part 1
  9. Video: Solving Rational Equations, Part 2
  10. Video: Solving an Equation Quadratic in Form
  11. Video: Solving Equations Involving Radicals

Graded: Rational Expressions
Graded: Rational and Radical Equations

WEEK 5


Functions. Graphs of Functions. Transformations of Functions.
In this module, we define the notion of "function". We learn to distinguish between functions and non-functions in graphical, symbolic and tabular form. Finally, we will explore graphs of functions and how these graphs behave under linear transformations.


13 videos, 3 readings expand


  1. 閱讀: Functions: Readings and Exercises
  2. Video: Introduction to Functions & Graphs
  3. Video: Relations versus Functions
  4. Video: Functions and the Vertical Line Test
  5. Video: Domain
  6. Video: Evaluating Functions
  7. 閱讀: Graphs of Functions
  8. Video: Finding the Domain and Range from a Graph
  9. Video: Domain and Intercepts
  10. Video: Difference Quotient
  11. Video: Piecewise-Defined Functions
  12. 閱讀: Transformation of Functions: Readings and Exercises
  13. Video: Increasing/Decreasing/Constant
  14. Video: Graph Transformations, Part 1
  15. Video: Graph Transformations, Part 2
  16. Video: Odd and Even Functions

Graded: Functions
Graded: Graphs of Functions
Graded: Transformations of Functions

WEEK 6


Quadratic Functions. Inverse Functions. Polynomials.
In this module, we explore quadratic equations and graphs. We also introduce the notion of inverse functions. Finally, we will learn about polynomial properties and practice some methods for polynomial root finding.


14 videos, 3 readings expand


  1. 閱讀: Quadratic Functions: Readings and Exercises
  2. Video: Equations of Quadratic Functions
  3. Video: Converting a Quadratic Function from Standard to Vertex Form
  4. Video: Graphing a Parabola, Part 1
  5. Video: Graphing a Parabola, Part 2
  6. Video: Maximum/Minimum Quadratic Function Word Problems
  7. Video: Quadratic Inequalities
  8. 閱讀: Inverse Functions: Readings and Exercises
  9. Video: Finding the Inverse of a Function
  10. Video: Inverse Functions
  11. Video: Verifying Inverse Functions
  12. 閱讀: Polynomials: Readings and Exercises
  13. Video: Polynomial Long Division
  14. Video: Synthetic Division
  15. Video: Properties of Polynomials
  16. Video: Remainder Theorem
  17. Video: Factor Theorem

Graded: Quadratic Functions
Graded: Inverse Functions
Graded: Polynomials

WEEK 7


Exponential and Logarithmic Equations.



Exponential and logarithmic functions are two important functions that are useful in applications of calculus. We will discuss properties and graphs of these special functions. We will also learn to solve equations involving exponential and logarithmic functions.


9 videos, 2 readings expand


  1. 閱讀: Exponentials and Logarithms: Readings and Exercises
  2. Video: Introduction to Exponential & Logarithmic Functions
  3. Video: Solving Exponential Equations
  4. Video: Change of Base Formula for Logarithms
  5. Video: Converting Between Logarithmic and Exponential Equations
  6. Video: Properties of Logarithms
  7. 閱讀: Exponential and Logarithmic Equations and Graphs: Readings and Exercises
  8. Video: Evaluating Logarithmic Expressions
  9. Video: Solving Logarithmic Equations
  10. Video: Exponential Graphs
  11. Video: Logarithmic Graphs

Graded: Exponentials and Logarithms
Graded: Exponential and Logarithmic Equations and Graphs

WEEK 8


Pre-Calculus Functions Final Exam
Now is your opportunity to review the topics from this course. The comprehensive final exam is your chance to demonstrate your conceptual understandings of functions and algebraic computational skills.




    Graded: Pre-Calculus Final Exam

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