Fundamental algebraic concepts are examined in the context of real world applications. Linear, quadratic, polynomial, exponential, and logarithmic functions are explored with emphasis on their numerical, graphical, and algebraic properties. Prerequisite: Grade of C or higher in MATH 106 OR a score of 21 or higher on the math portion of the ACT (or if the ACT was taken before September 1989, a score of 20) OR a score of 500 or higher on the math portion of the SAT OR a passing score on the Columbia College math placement exam.
Prerequisite(s) / Corequisite(s):
Grade of C or higher in MATH 106 or a score of 21 or higher on the math portion of the ACT (or if the ACT was taken before September 1989, a score of 20) or a score of 500 or higher on the math portion of the SAT or a passing score on the Columbia College math placement exam.
Course Rotation for Day Program:
Most current editions of the following:
College Algebra in Context
By Harshbarger and Yocco (Pearson) Recommended
Essentials of College Algebra with Modeling and Visualization
By Rockswold (Pearson) Recommended
Functions and Change
By Crauder (Cengage) Recommended
Course Learning Outcomes
Work with functions defined numerically, symbolically, graphically, or verbally.
Analyze characteristics of functions, such as end behavior, intercepts, and extreme values, from its rule, graph, or table of values.
Compute the inverse of a function, when one exists, and demonstrate the meaning of the inverse graphically and algebraically.
Solve real world problems using linear, quadratic, polynomial, rational, exponential, and logarithmic models and interpret the solutions.
Solve linear, quadratic, polynomial, rational, exponential, and logarithmic equations and systems of equations algebraically, graphically, and with technology.
Major Topics/Skills to be Covered:
Define functions as special types of relations.
Describe the concept of a function using numerical, graphical, verbal and symbolic perspectives.
Analyze characteristics of a function from its graph or table of values, such as long-term and extreme behavior.
Combine functions arithmetically and through composition.
Describe the fundamental concepts associated with inverse functions including the definition of one-to-one functions and the graphical interpretation of inverses.
Use technology to find lines of best fit and interpret the results.
Use lines and systems of linear equations to model real-world situations.
Solve systems of equations algebraically, graphically, and with technology.
Define exponential and logarithmic functions and use them to model real-world situations.
Solve equations with exponential and logarithmic expressions using properties of logarithms and technology.
Define polynomial functions and use them to model real-world situations.
Solve nonlinear equations using factoring and technology.
State the definition of complex numbers and their arithmetic rules.
Use technology to model data using quadratic regression.
Identify and interpret the vertex of a parabola using algebra and technology.
Define rational functions.
Identify and interpret the asymptotes of rational functions using algebra and technology.
Determine an appropriate function to model real world phenomena or events.
Interpret fundamental concepts of linear functions such as slope and intercepts.
Solve quadratic equations using factoring, the quadratic formula and technology.
Recommended maximum class size for this course: 30
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section.
However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.