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# COURSE OUTLINE FOR PRECALCULUS

Catalog description (2006-2009 Catalog):

A second course in the mathematics sequence leading to calculus for engineering, computer science, math, and science majors. In depth study of polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions, equations, and identities; systems of equations including matrices; extensive use of graphing calculators.

Is course New, Revised, or Modified?

Revised Fall 2008

Required texts/other materials:

Text: Barnett, Ziegler, Byleen and Sobecki. Precalculus: Graphs and Models, 3rd Edition ( McGraw-Hill)

Graphing calculator required. TI-83, 84, 86, or comparable model strongly recommended. No calculator with computer algebra systems (CAS) is permitted.

Information resources:

The library has an extensive collection of books that students may use for extra reinforcement of the course content.

Other learning resources:

MathZone, and online tutorial resource, is also made available to students enrolled in the course. Tutoring is available at the Learning Center on both campuses. Both libraries have copies of the textbook.

Course Competencies/Goals:
The two primary goals of this Precalculus course are to prepare students for calculus, and to develop a
comprehensive understanding that functions are statements of how a change in one quantity brings about a change
in another quantity. To that end, students will develop quantitative and logical skills enabling them with the ability to
effectively interpret and communicate mathematical results, both in abstract and contextual settings that arise in
everyday life.

The student will be able to:
I. Demonstrate in-depth knowledge of polynomial, rational, exponential, logarithmic, trigonometric, inverse
trigonometric functions, expressions, equations and identities

II. Generate and interpret the graphs of polynomial, rational, exponential, logarithmic, trigonometric and
inverse trigonometric functions

III. Generate and apply models of events in our daily life from which predictions can be made using data
and technology

IV. Demonstrate the understanding that given certain conditions under which two or more quantities are
related, optimum solutions to problems can be obtained graphically and algebraically

V. Demonstrate the understanding that mathematics plays an important role in various fields through the
ability to transfer mathematical algorithms and techniques from problems in one field to that of another

VI. Analyze and solve word/applications problems, applying quantitative estimations when appropriate

VII. Demonstrate proficiency in the use of graphing calculator technology

Course-specific General Education Knowledge Goals and Core Skills.

General Education Knowledge Goals
Goal 2. Mathematics. Students will use appropriate mathematical and statistical concepts and operations to interpret
data and to solve problems.

Goal 4. Technology. Students will use computer systems or other appropriate forms of technology to achieve
educational and personal goals.

MCCC Core Skills
Goal A. Written and Oral Communication in English. Students will communicate effectively in speech and
writing, and demonstrate proficiency in reading.

Goal B. Critical Thinking and Problem-solving. Students will use critical thinking and problem solving skills in
analyzing information.

Units of study in detail.

Unit I [Operations on Functions, Compositions, Polynomial & Rational Functions] – 4 weeks
Learning Objectives
The student will be able to…

• Find the sum, difference, product and quotient of two given functions, giving the domain of each
(CG I, GE 2,B)

• Find the composite of two given functions and determine the domain of the composite (CG I,
GE 2,B)

• Determine the values of operations on functions or the value of the composite function when
given the graphs of two functions and given an input value (CG I, II, GE 2, B)

• Find two functions, f and g, such that f ◦ g = h for a given function h (CG I, GE 2,B)

• Determine whether a given set of ordered pairs, given graph, or given equation corresponds to
a one-to-one function (CG I,II,VII, GE 2,4,B)

• Find the inverse and its domain and range of a given one-to-one function and verify that the two
functions f (x) and g(x) are inverses of each other by showing f (g(x)) = x and
g( f (x)) = x (CG I,II, GE 2,4,B)

• Graph a function and its inverse on the same axes and graph the line of symmetry y = x (CG
I,II,VII GE 2,4,B)

• State and apply the Division Algorithm, Remainder Theorem, Factor Theorem, Fundamental
Theorem of Algebra, n Linear Factors Theorem, Rational Zeros Theorem, Imaginary Zeros
Theorem, Upper and Lower Bound Rules for Real Zeros (cover this last theorem lightly) (CG
I,II, GE 2,B)

• Perform algebraic long division and synthetic division of polynomials (CG I, GE 2,B)

• Evaluate a polynomial by using the remainder theorem and synthetic division (CG I, GE 2,B)

• Determine the left and right end behavior of a polynomial using the degree and leading
coefficient (CG I,II,VII GE 2,B)

• Sketch the graph of a polynomial or rational function and confirm the sketch by choosing an
appropriate viewing window on the graphing calculator (CG I,II,VII, GE 2,4,B)

• Find all real zeros of a polynomial or rational function and confirm the zeros by using the “root”
or “zero” function on the graphing calculator (CG I,II,VII, GE 2,4,B)

• Use the maximum and minimum functions on the graphing calculator to find the local extrema
of a given polynomial (CG I,II,VII, GE 2,4,B)

• Describe the behavior of the graph of a polynomial at a zero with an odd or even multiplicity
(CG I,II,, GE 2,4,A, B)

• Write an equation of a polynomial having given zeros and a given degree (CG I,II, GE 2, A, B)

• Find, if possible, all the zeros and their multiplicity of a polynomial function with real coefficients
and write the polynomial as a product of linear and irreducible quadratic factors over the real
numbers using various methods, including the Rational Zeros Theorem (CG I,II, GE 2, A, B)

• Approximate irrational zeros for a polynomial using the bisection method for odd multiplicity
zeros or a maximum or minimum approximation for even multiplicity zeros to two decimal
places (CG I, II, GE 2,B)

• Find the vertical, horizontal, and/or slant/oblique asymptotes, if any, for a rational function (CG
I, II, GE 2,B)

• Solve applications that result in equations which are polynomial or rational functions and
interpret findings in the context of the application (CG III, VI, GE 2,A,B)

• Use graphing calculator technology to accomplish these tasks, where applicable (CG I, II, III,
VI, VII, GE 2,4,B)