SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

Department: Mathematics

Subject Area and Course Number: Mathematics 137

Course Title: Precalculus I–College Algebra & Functions

Discipline: Mathematics

Units: 5

Repeatability: None

Catalog Course Description: Short review of intermediate algebra topics; extensive treatment of functions and graphing techniques, including translations, symmetries, reflections and graphs of inverse functions. Identities and conditional equations. Analysis and applications of polynomial, rational, exponential and logarithmic functions. Solving linear and non-linear systems, using matrix algebra, and roots of higher-degree polynomials. Logic and structure of proofs.

Description for Schedule of Classes: Extensive treatment of functions and graphing, including polynomial, rational, exponential and logarithmic functions. Solving linear and non-linear systems, matrix algebra and finding roots of higher-degree polynomials. Study of logic and proofs.

Lecture Hours per Week: 5.3 (80-90 Total Semester Hours)

Laboratory Hours per Week: None

Plus Hours: None

Prerequisites: Math 111 or Math 120, with grade of “C” or better or qualifying score on SBCC placement exam.

Co-requisites: None

Skills Advisories: Eligibility for English 100 or English 103

Course Advisories: None

Limitation on Enrollment: None

Course Objectives: At the end of this course, the student will be able to:

1. Demonstrate familiarity with the notation and key properties associated with functions in general, whether the functions are represented algebraically or graphically.

2. Analyze and solve problems involving algebraic fundamentals, functions, and graphs.

3. Demonstrate a beginning ability to present clear and logical solutions to the above problems.

4. Use graphing technology such as graphing calculators or computer software to create graphs and tables of values for algebraic and transcendental functions.

Course Content and Scope:

1. Review of algebraic fundamentals

a. Exponents

b. Polynomial--Factoring

c. Radicals

d. Linear Equations and Applications

2. Functions and Graphing

a. Graphs, functions, and relations – an introduction

b. Distance formula and equation of a circle

c. Linear and quadratic functions

d. Symmetry and translations – supplements may be needed

e. Expansions and contractions – supplements needed

f. Algebra of functions – function compositions

g. Inverse functions

3. Graphing polynomial and rational functions

a. Polynomial and rational inequalities

b. Finding zeroes of polynomials (factor and remainder theorems & synthetic division)

c. Graphs of polynomial functions

d. Graphs of rational functions

4. Systems of linear equations and matrices

a. Review of linear systems

b. Matrices and their applications to linear equations

c. Determinants

d. Partial fraction decomposition

5. Logic and Proof

a. Sets and set operations

b. Open statements, quantifiers, and Venn diagrams

c. Disjunction, conjunction, negation, implication and equivalence

d. Direct and indirect proofs

6. Exponential and logarithmic functions

a. Exponential functions and their graphs

b. Logarithmic functions and their graphs

c. Exponential and logarithmic equations

d. Applications

Methods of Instruction: Lecture is the primary activity, along with student problem-solving activities. Students are also expected to work outside of class on assigned exercises and supplemental reading from the text.

Required Assignments:

A. Appropriate Readings: Students are required to read assigned sections in text or supplements.

B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols.

C. Appropriate Outside Assignments: Students are expected to spend a sufficient amount of time outside of class to practice techniques presented during class time, read assigned materials, and complete frequent homework assignments.

D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. They must also analyze using both inductive and deductive reasoning within a logical system.

Methods of Evaluation: A student’s grade will be based upon multiple measures of performance in the solving of algebraic problems, in the preparation and in the analysis of graphs, and analysis of logical arguments. Such measures may include at least four one-hour exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student’s dexterity with algebra skills and familiarity with mathematical vocabulary.

In accordance with district policy, instructors are to provide students a written course syllabus which will

include the specific procedures by which students will be evaluated. These procedures must be consistent with

the objectives and course content stated above.

Appropriate Texts and Supplies:

Cohen, Precalculus with Unit-Circle Trigonometry, 4^th Ed., Cengage Publishing, 2006

Edmondson, Logic and Proof for Algebra, Santa Barbara City College, 1987

TI-84 Graphing Calculator

Student Learning Outcomes:

1. Identify properties of functions and their graphs, including symmetry, translations, expansions, contractions, the algebra of functions and composition, and inverse functions.

2. Determine general polynomial behavior, and apply polynomial properties to solve equations and inequalities, both graphically and algebraically.

3. Solve systems of linear and nonlinear equations, and apply these methods to solve application problems.

4. Apply properties of exponential and logarithmic functions to solve application problems.

IA/mej

Revised August 2006; 8/24/09

FRC (WPC)