**Description
**

In this course, students will develop skills in the analysis of functions and solving of

equations and inequalities. The function concept will be central, with the focus on

preparing students for calculus. Polynomial, rational, exponential, logarithmic and

trigonometric functions will be studied in detail. Additional topics include complex

numbers, conic sections, sequences and series, and parametric equations. Modeling using

data analysis will be an integral part of this course. A graphical approach will be utilized

throughout, with an emphasis on solving application problems. A graphing calculator is

required and the computer algebra system DERIVE will also be used. Not open to

students who have completed MATH 131 or MATH 133. MATH 135 is equivalent to

MATH 131 and 133.

Upon completion of this course, the student will be able to:

1. Use the basic properties and rules of the real number system to solve problems

involving radical and absolute value expressions.

2. Evaluate and graph functions, some of which are altered by shifts, reflections, and/or

transformations.

3. Perform the basic operations on or find the composite of two or more functions.

4. Find and graph the inverse of a function.

5. Solve absolute value and non-linear inequalities.

6. Apply classic theorems to find the zeros of polynomial equations and graph its

corresponding function.

7. Operate with complex numbers in standard (rectangular) form.

8. Graph rational functions.

9. Use exponents and logarithms to solve equations and application p problems.

10. Define and graph the trigonometric functions and their inverses.

11. Prove or disprove trigonometric identities and solve trigonometric equations.

12. Apply area, sum and difference, double angle, half-angle trigonometric formulas and

the standard trigonometric identities.

13. Use the Law of Sines and Cosines.

14. Operate with complex numbers in trigonometric form.

15. Apply DeMoivre’s Theorem

16. Find polynomial, exponential and trigonometric models that best fit a set of data.

17. Apply and graph parametric equations.

18. Determine and apply arithmetic and geometric sequences

19. Manipulate series and summation notation

17. Solve application problems.

18. Use a scientific programmable graphing calculator in solving problems.

**Major Topics**

I. Graphs, Functions, and Models

A. Functions, and Graphs

B. Slope (Rate of Change)

C. Curve Fitting, and Linear Regression

D. Analysis of Functions

E. Symmetry and Transformations

F. Circles

II. Functions and Equations: Zeros and Solutions

A. The Complex Numbers

B. Quadratic Like Functions

C. Analyzing Graphs of Quadratic Functions

D. Quadratic Regression

E. Radical and Absolute Value Equations

F. Solving Inequalities

III. Polynomial and Rational Functions

A. Polynomial Functions and Modeling

B. Polynomial Division; The Remainder and Factor Theorems

C. Theorems about Zeros of Polynomial Functions

D. Rational Functions

E. Polynomial and Rational Inequalities

IV. Exponential and Logarithmic Functions

A. Composite and Inverse Functions

B. Exponential Functions and Graphs

C. Logarithmic Functions and Graphs

D. Properties of Logarithmic Functions

E. Solving Exponential and Logarithmic Equations

F. Applications and Models: Growth and Decay

V. Trigonometry

A. Right Triangle Trigonometry

B. Trigonometric Functions, Their Inverses, and Graphs

C. Solving Equations and Verifying Identities

D. Sum and Difference, Double Angle, and Half-Angle Formulas

E. Law of Sines and Cosines

G. Trigonometric Form of a Complex Number

H. DeMoivre's Theorem and Nth Roots

VI. Analytic Geometry

A. Properties of Conic Sections and Graph

B. Standard Equation of a Conic Curve

C. Parametric Equations

VII. Sequences and Series

A. Basic and Recursive Definitions

B. Arithmetic and Geometric Sequences

C. Finite and Infinite Series

**Course Requirements**

**Required Text: **Contemporary Precalculus: a Graphing Approach by Thomas

Hungerford

**Required Calculator: **Graphing Calculator (TI-83, TI-83+ or TI-84
recommended)

A calculator with a computer algebra system, like the TI-86, will not be allowed
on tests.

**Required Computer Usage:** Derive (a computer algebra system), available in
class and

in the computer labs.

**Grading/Exams:** Grading procedures will be determined by the individual
faculty

member but will be based on several unit exams and a comprehensive final exam.

**Other Course Information**

MATH 135 is a prerequisite course for the main calculus sequence, MATH 140/150 ,

intended primarily for mathematics, science and engineering majors. If you are a

business, social science or humanities major, your interests may be better
served by

taking MATH 145 (Business Calculus) or MATH 138 (Statistics). Contact the
counseling

center and your transfer institution for more specific information.

This course is a Math core course and an Arts and Science elective.

Transferability: MATH 135 generally transfers to four-year institutions. Contact

the counseling center for specific information.