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
Elective Requirements: Fulfills Academic Electives
Integrative Experience Requirement: No

Student Learning Outcomes

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

Course Contents

Analyzing functions: Domain and range. Even and odd functions. Graphs of parent functions. Extrema.
Transformations of functions: Shifts. Scaling. Reflections.
Composite functions. One-to-one functions. Inverse functions.
Piecewise functions: Graphs. Identify and classify discontinuities.
Polynomials: Factor Polynomials. Find the zeroes of polynomials (real and complex). Graph polynomials (end behavior, turns, zeros). Solve optimization applications.
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.
Difference quotient: Find the difference quotient of polynomial, radical, and rational functions.
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