MATH& 141 - Precalculus I

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: Precalculus I is the study of functions including piecewise, polynomial, rational, exponential and logarithmic functions and their graphs; systems of equations; inequalities; curve sketching and transformations. Graphing technology is required.

Prerequisite: MATH 099 with a grade of C or higher, or equivalent math placement score.
Distribution Requirements:

Natural Sciences Distribution Requirement
Quantitative

General Education Requirements:

Fulfills Quantify General Education Requirement

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Graph polynomial, rational, exponential, logarithmic, and piecewise functions.
Describe key features of a function, such as discontinuities, asymptotes, domain, and range.
Analyze polynomials using the Fundamental Theorem of Algebra.
Solve polynomial, rational, exponential, and logarithmic equations using analytic or graphical techniques.
Find composite and inverse functions.
Identify and classify extrema using a graph.
Solve systems of equations using matrices.
Find the difference quotient of polynomial, radical, and rational functions.
Apply common transformations of functions.
Solve nonlinear inequalities.

Course Contents

Functions. Graphs of parent functions. Find the domain and range of a function. Graphs of piecewise functions, discontinuities. Transformations: shifts, scaling, and reflections. Composite functions. One-to-one and inverse functions.
Polynomials. Factor Polynomials. Solve optimization applications. Graph polynomials (end behavior, turns, zeros). Find the zeroes of polynomials (real and complex).
Rational Functions. Graph rational functions using asymptotes, intercepts, and holes.
Exponential and Logarithmic Functions. Graphs of exponential and logarithmic functions. Properties of logarithms. Solve exponential and logarithmic equations. Applications using exponential and logarithmic models.
Systems of Equations. Solve systems in two or three variables. Solve systems of equations using matrices. Solve systems of non-linear equations (optional). Applications of systems of equations.
Non-linear Inequalities. Solve non-linear inequalities.

Instructional Units: 5