# 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, 3^{rd} 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)