Pre-Calculus: Functions

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

每門課程都像是一本互動的教科書，具有預先錄製的視頻、測驗和項目。

來自同學的幫助

與其他成千上萬的學生相聯繫，對想法進行辯論，討論課程材料，並尋求幫助來掌握概念。

證書

獲得正式認證的作業，並與朋友、同事和雇主分享您的成功。

University of California, Irvine Since 1965, the University of California, Irvine has combined the strengths of a major research university with the bounty of an incomparable Southern California location. UCI’s unyielding commitment to rigorous academics, cutting-edge research, and leadership and character development makes the campus a driving force for innovation and discovery that serves our local, national and global communities in many ways.

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