Catalogue Description: College Algebra emphasizes the notion of functions as a unifying concept. The following families of functions and their characteristics are examined within this course: polynomial, rational, exponential and logarithmic functions. Additional topics will include solving inequalities and systems of nonlinear equations. Writing assignments, as appropriate to the discipline, are part of the course. Applications involving problem-solving skills will be emphasized throughout the course. The included curriculum is broken into 6 units.
Students the Course is Expected to Serve: This course is intended for students who plan to major in business, mathematics, engineering, and science.
1. Analyze the graphs of various families of functions.
2. Apply the models and characteristics of various families of functions to scenarios in order solve real-world (contextual) problems.
Student Learning Outcomes: Upon satisfactory completion of the course, students will be able to:
A. Polynomial Functions. Identify the characteristics of a quadratic function (i.e., vertex, axis of symmetry, and direction of concavity).
B. Compute roots/zeros of a polynomial function by factoring techniques.
C. Estimate the roots/zeros of a polynomial function.
D. Solve polynomial inequalities.
E. Solve systems of linear equations using matrices and determinants.
F. Solve systems of linear inequalities.
G. Solve systems of nonlinear equations.
H. Rational Functions. Simplify rational expressions using the division algorithm.
I. Identify points of discontinuity of a rational function.
J. Identify vertical/horizontal asymptotes and end behavior of rational functions.
K. Solve rational inequalities.
L. Exponential and Logarithmic Functions. Define exponential and logarithmic functions.
M. Simplify exponential and logarithmic expressions using their properties.
N. Solve exponential and logarithmic equations.
O. Formulate and apply exponential and logarithmic functions to a contextual situation.
P. It is expected that the following student learning outcomes (Characteristics of Functions) will be embedded, as appropriate, in the study of the family of functions listed above. Identify the domain and range of a function.
Q. Determine intervals on which functions are decreasing/increasing, continuous/non continuous, or piecewise.
R. Identify functions from multiple sources of information (i.e., verbal descriptions, graphs, equations, and tables of values).
S. Relate the effect of transformations (i.e., translations, rescaling, or reflections) on graphs of functions and their corresponding equations.
T. Perform operations (i.e., addition, subtraction, multiplication and division) on functions, including the composition of functions.
U. Decompose a function into a composition of two or more functions.
V. Formulate and apply a function to a contextual situation.
W. Determine the conditions under which a function has an inverse.
X. Identify the inverse of a function from multiple representations.
Y. Reformulate a given function into various representations (i.e., verbal, graphical, algebraic, or tabular).
Topical Outline: The course will cover the following topics:
2. Linear Functions
3. Polynomial and Rational Functions
4. Exponential and Logarithmic Functions
5. Systems of Equations (Matrices Included)
6. Sequences and Series
A more detailed breakdown of topics and curriculum outline can be found here.