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PRECALCULUS: FUNCTIONS AND GRAPHS

1.

Course Number Course Title Semester Units Hours
MATH 179 Precalculus:
Functions and
Graphs
5 5 hours lecture
1 hour lab

2. Catalog Description
Graphic, numeric, and analytic approaches to the study of precalculus concepts from
college algebra and analytic trigonometry. Use of trigonometric equations, theorems, and
identities to solve vector, right triangle, and oblique triangle problems. Application of
appropriate technology including but not limited to computer programs and graphing
utilities to model, analyze, and interpret a collection of data or to solve real-world
application problems from a wide variety of disciplines. Topics include the real number
system; algebraic, exponential, and logarithmic functions and their inverses; graphing
techniques for polynomial, rational, and trigonometric functions; complex numbers;
theory of equations; trigonometric functions and their inverses with emphasis on the
circular functions; trigonometric equations and identities ; vectors; partial fractions; polar
coordinates; mathematical induction; sequences and series; matrices; and the binomial
theorem. A student can earn a maximum of 6 units for successfully completing any
combination of MATH 170, MATH 175, and MATH 179.

3. Course Prerequisites
A grade of "C" or better in MATH 110 or equivalent and MATH 097 or equivalent.
(MATH 103 does not meet the prerequisite for this course ).

4. Entrance Skills
a. Identifying and/or simplifying :
1. Linear, quadratic, rational, radical, absolute value, exponential, and
logarithmic equations
2. Polynomial expressions
3. Rational expressions
4. Algebraic expressions involving radicals and/or rational exponents
5. Logarithmic expressions
6. Complex numbers
7. Basic mathematical formulas from related disciplines

b. Solving:
1. Algebraic equations
2. Logarithmic and exponential equations
3. Systems of equations and inequalities
4. Applications from a wide variety of disciplines

c. Graphing, Transforming, and/or Operating on the following:
1. Polynomial absolute value, exponential and logarithmic functions and
their inverses
2. Linear and quadratic inequalities
3. Systems of equations and inequalities

d. Factoring polynomials

e. Functions:
1. Determine the domain and range
2. Find the inverse
3. Perform basic operations

f. Geometry:
1. Formulas for geometric objects
2. Properties of geometric figures

g. Mathematical Reasoning and Problem Solving:
1. Inductive and deductive reasoning
2. Effective communication of mathematical arguments

5. Course Objectives

  Students successfully completing MATH 179 will be able to:
 
Comp. 4
Box 1d
a. analyze linear, quadratic, polynomial, rational, absolute value, exponential,
logarithmic, and trigonometric functions and their inverses from a graphic,
numeric, and analytic perspective
 
Comp. 5
Box 2e
b. analyze and solve applied problems from various disciplines and involving a wide
variety of equations including but not limited to: linear, quadratic, polynomial,
rational, radical, absolute value, exponential, logarithmic, and trigonometric
equations
 
Comp. 3 &
Comp. 4
Box 1a & 1f
c. apply critical thinking and mathematical reasoning skills necessary in collegiatelevel
algebraic problem solving in related disciplines such as science, business,
and engineering
 
  d. use the techniques of analytic geometry to graph conic sections
 
Comp. 4
Box 2c
e. observe, interpret, and analyze the behavior of graphs of a wide variety of
functions and statistical plots including the trigonometric functions
 
  f. use sequences and series to solve theoretical and applied problems from various
disciplines such as science, business, and engineering
 
Comp. 5
Box 4e
g. use phase shift to illustrate translation of trigonometric functions including
amplitude if applicable
 
  h. find the principal domain and range of the trigonometric functions
 
  i. use arclength and radian measure to analyze the trigonometric functions
 
  j. apply the trigonometric identities in solving trigonometric equations
 
  k. use trigonometric equations, theorems, and identities to solve vector, right
triangle, and oblique triangle problems, and
 
Comp 1&
Comp 4
Box 5h &
Comp 5
Box 4b 7 4c
l. select and apply appropriate technology including but not limited to computer
programs and graphing utilities to model, analyze, and interpret a collection of
data or to solve real-world application problems requiring the use of collegiatelevel
mathematics.

6. Minimum Instructional Facilities

a. Standard mathematics classroom equipped with:
1. Whiteboards covering three walls
2. Graphing utility overhead viewing panels
3. Multimedia computer stations with projections capabilities, and a
projection screen.

b. Basic skills math lab equipped with:
1. Whiteboard
2. Pull-down projection screen
3. Computer work-station for each student
4. Appropriate mathematical software
5. Word processor, spreadsheet, and other work-place software
6. Instructor’s work station with multimedia projection capabilities

7. Minimum Student Materials
a. Graphing utility
b. Floppy disk
c. Portfolio

8. Course Content

  a. Linear, quadratic, polynomial, rational, absolute value, exponential,
logarithmic, and trigonometric functions, their graphs and their inverses

b. Graphic, numeric, and analytic methods to solve application problems
including linear, quadratic, polynomial, rational, absolute value,
exponential, logarithmic and trigonometric equations

c. Polynomial and rational functions and equations including the use of
graphing utilities and synthetic division to graph

d. Trigonometric functions developed from the unit circle using radian and
degree measure

e. Trigonometric identities

f. Graphic, numeric, and analytical methods to solve linear and non-linear
systems of equations and inequalities

g. Matrices and determinants

h. Sequences and series

i. Binomial theorem

j. Mathematical induction

k. Conics, parametric equations, and polar coordinates

l. Vectors in a plane

Comp. 6
Box 3e
m. Historical contributions of number and mathematical theories and
concepts from diverse cultures.

9. Method of Instruction

Comp. 6
Box 1a &
1c
a. Lecture
b. Team work
c. Discussion
d. Integrated computer instruction

10. Methods of Evaluation

Comp. 2 &
Comp. 4
Box 3d
a. Independent exploration activities evaluated and graded by the instructor
b. Midterms and final exam will include questions designed to evaluate
students’ grasp of concepts and mastery of skills
c. Final exam to be comprehensive and taken in-class.

11. Texts
Required text:
a. T Varberg, D. Varberg. Precalculus: A Graphing Approach. Prentice Hall
Press, 1995.

Supplementary text/workbook:
b. Heath and Company, 1996.

10. Exit Skills
A. Identify and/or perform
1) Domain and range of algebraic and trigonometric functions
2) Operations of algebraic and trigonometric functions
3) Inverses of algebraic and trigonometric functions
4) Operations with complex numbers
5) Trigonometric form of complex numbers

B. Solve
1) Algebraic and absolute value equations and inequalities
2) Logarithmic and exponential equations
3) n^th order systems of equations and inequalities
4) Application problems involving oblique triangles, the Pythagorean
Theorem, Law of Sines , Law of Cosines, and vectors
5) Trigonometric equations using the basic trigonometric identities
6) Application problems from variety of disciplines
7) Application problems involving right triangle trigonometry

C. Interpret from a graphical, numerical, and/or analytic perspective:
1) Trigonometric functions developed from the unit circle using radian or
Degree measure
2) Inverse trigonometric functions
3) Amplitude, period, frequency, and phase shift of trigonometric functions
4) Algebraic functions and their inverses including: polynomial, radical,
rational, absolute value, exponential, and logarithmic functions
5) Linear and quadratic inequalities
6) Systems of equations and inequalities

D. Apply inductive and/or deductive reasoning and the basic trigonometric identities
to verify other trigonometric identities
 

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