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Posted : 05/16/07

MAT 194 - Precalculus

Course Description

This course prepares students for Calculus. The topics discussed include an intensive study of polynomial, rational, exponential, logarithmic, and trigonometric functions and their graphs. Applications include simple maximum and minimum problems, exponential growth and decay.

Competency Areas		Hours
Functions Polynomial and Rational Functions Exponential and Logarithmic Functions Trigonometric Functions Applications of Trigonometry		Class/Week D. Lab/Week P. Lab/Week Credit Hours	5 0 0 5
Prerequisite:	MAT 191 with a grade of C or better.

Course Guide

Competency	After completing this section, the student will:	Hours
		Class	D.Lab	P.Lab
Functions		5	0	0
Introduction to Functions	Define a function and terminology associated with a function such as domain and range; maximum and minimum values; increasing, decreasing, and constant functions; end behavior of a function; zeros and roots of a function; and transformation of a function.
Introduction to Graphing Calculator	Use the graphing calculator to graph functions.
Linear Functions	Define a linear function. Graph a linear function. Solve application problems involving linear functions.
Quadratic Functions	Define a quadratic function. Determine the vertex and the maximum and minimum values of a quadratic function. Graph a quadratic function. Solve application problems involving quadratic functions
Algebra of Functions	Add functions. Subtract functions. Multiply functions. Divide functions. Form and evaluate composite functions. Find the inverse of a function.
POLYNOMIAL AND RATIONAL FUNCTIONS		10	0	0
Polynomial Functions	Define a polynomial function. Use the leading term test to determine the left and right behavior of a polynomial function. Find all the zeros of a polynomial function including complex zeros. Graph polynomial functions and their transformations
Rational Functions	Define a rational function. Determine the domain and range of a rational function. Determine the vertical and horizontal asymptotes of a rational function Graph rational functions and their transformations.
EXPONENTIAL AND LOGARITHMIC FUNCTIONS		10	0	0
Exponential Functions	Define an exponential function. Evaluate an exponential function. Determine the domain and range of an exponential function. Graph exponential functions and their transformations. Use exponential functions to model certain phenomena in nature such as exponential growth and decay and in practical situations such as money invested at compound interest
Logarithmic Functions	Define a logarithm. Apply the properties of logarithms to determine the values of logarithmic expressions and to solve logarithmic and exponential equations. Define a logarithmic function. Determine the domain and range of a logarithmic function. Graph logarithmic functions. Solve application problems involving logarithmic functions.
TRIGONOMETRIC FUNCTIONS		20	0	0
Circular Functions	Define the six circular functions Determine the domain and range of the circular functions. Graph the circular functions using amplitude, period, and phase shift
Trigonometric Functions	Define the six trigonometric functions. Use the trigonometric functions to solve right triangles. Solve application problems involving right triangles. Use the law of sines and the law of cosines to solve oblique triangles. Solve application problems involving oblique triangles. Use the fundamental trigonometric identities, sum and difference identities, and double- and half-angle identities to prove identities. Determine the domain and range of the trigonometric functions and their inverses. Graph the trigonometric functions and their inverses.
APPLICATIONS OF TRIGONOMETRY		5	0	0
Vectors	Define a vector. Find the components of a vector. Perform operations on vectors. Solve application problems involving vectors.
Complex Numbers	Define a complex number. Express complex numbers in standard, rectangular, polar, and trigonometric forms. Graph complex numbers on the Argand diagram. Perform operations with complex numbers. Use DeMoivre Theorem to find powers and roots of complex numbers.

Suggested Resources

Aufmann, Barker, & Nation (1993). Precalculus. (2^nd ed.).Boston: Houghton Mifflin.

Barmett, Ziegler & Byleen (1999). Precalculus Functions and Graphs. (4^th ed.) Boston: McGraw Hill.

Bittinger, Beecher, Ellenbogen, & Penna (2001). Precalculus Graphs and Models: A Unit Circle Approach. Boston: Addison Wesley.

Bittinger, Beecher, Ellenbogen, & Penna (2001). Precalculus Graphs and Models (2^nd ed.). Boston: Addison Wesley.

Blitzer (2001). Precalculus. Englewood Cliffs: Prentice Hall.

Demana, Waits, Foley, & Kennedy (2001). Precalculus Functions and Graphs (4^th ed.). Boston: Addison Wesley.

Dugopolski (1999). College Algebra and Trigonometry. (2^nd ed.). Boston: Addison Wesley.

Larson, Hoestetler, & Edwards (2000). Precalculus Functions and Graphs: A Graphing Approach (3^rd ed.). Boston: Houghton Mifflin.

Lial, Hornsby, & Schneider (2001). College Algebra and Trigonometry and Precalculus (2^nd ed.). Boston: Addison Wesley.

Lial, Hornsby, & Schneider (2001). Precalculus With Limits. Boston: Addison Wesley.

Sullivan & Sullivan (2000). Precalculus Enhanced With Graphing Utilities. Englewood Cliffs: Prentice Hall.