Course Number: MATH 1111

 

Course Title: College Algebra

 

Hours Credit: 3 hours

 

Prerequisites: None

 

Courses Description: This course is a functional approach to algebra that incorporates the use of technology. Emphasis will be placed on the study of functions, and their graphs, inequalities, and linear, quadratic, piece-wise defined, polynomial, rational, exponential and logarithmic functions. Appropriate applications will be included.

 

Text: Precalculus (3^rd edition) by Robert Blitzer, Prentice-Hall

 

Learning Outcomes: Students should be able to demonstrate:

1. An understanding of the equations of circles and lines
2. An understanding of functions and how to graph functions
3. An understanding of operations on functions including function composition
4. An understanding of polynomial and rational graphs, including intercepts and asymptotes
5. An understanding of how to find the zeros of a polynomial and how to factor polynomials
6. An understanding of inverse functions and how to find them graphically and algebraically
7. An understanding of the properties of exponential and logarithmic equations
8. An understanding of how to solve exponential and logarithmic equations
9. An understanding of how to solve a system of equations

 

Topics: (for a listing of topics and problems to be covered in each section, see pages 6-10)

NOTE: Review Topics for the first week of class should be chosen from:

            P.5       Factoring Polynomials

            P.6       Rational Expressions

            P.7       Equations

            P.9       Linear Inequalities and Absolute Value Inequalities

            1.1       Graphs and Graphing Utilities

 

The following sections must be covered:

 

SECTION        TOPIC                                                                                    

                       

1.2                   Basics of Functions and Their Graphs                          

1.3                   Graphs of Functions and Their Graphs                        

1.4                   Linear Functions and Slope                                                     

1.5                   More on Slope                                                                        

1.6                   Transformations of Functions                                     

1.7                   Combinations of Functions; Composite Functions                   

1.8                   Inverse Functions                                                                                

1.9                   Distance and Midpoint Formulas; Circles                                 

2.1                   Complex Numbers                                                                   

2.2                   Quadratic Functions                                                                

2.3                   Polynomial Functions and Graphs                                                       

2.4                   Dividing Polynomials                                                  

2.5                   Zeros of Polynomials ( Optional Topics include:

Rational Root Theorem and Descartes’ Rule

of Signs if TIME PERMITS)

2.6                   Rational Functions

3.1                   Exponential Functions

3.2                   Logarithmic Functions

3.3                   Properties of Logarithms

3.4                   Exponential and Logarithmic Equations

3.5                   Exponential Growth and Decay; Modeling Data

7.1                   Systems of Linear Equations in Two Variables

7.2                   Systems of Linear Equations in Three Variables

7.4                   Systems of Nonlinear Equations in Two Variables

 

Grading Method: To be determined by instructor. The final exam should be given during the time as scheduled by the Registrar’s Office and should count between 20% and 35% of the overall grade.