Prerequisite: Mathematics 105 or 114 (with a grade of C or
better) or satis factory score on the College
Level Math Placement Test within last calendar year
Advisory: English Writing 211 and Reading 211 (or Language Arts 211), or English
as a Second
Language 272 and 273.
5 hours lecture
Course Description
Polynomial, rational, exponential and logarithmic functions , graphs, solving
equations.
Course Philosophy
The sequence of three courses in precalculus mathematics is intended to provide
the student who has
successfully completed intermediate algebra with the foundations needed for
success in calculus and
advanced courses in mathematics and the sciences. Throughout the sequence, the
courses emphasize
building analytical and quantitative skills and the mathematical maturity
necessary for solving problems
in mathematics and related fields. Specifically, the student will define
variables and use them to write,
analyze and graph functions and other relations which occur in modeling and
other applications. The
student will also develop skills in solving equations and inequalities. The
material is rich in applications,
both modern and classic, drawn from historical and multicultural origins of the
topics and modern
applications in many fields.
Various elementary functions are studied and used to model application problems
in mathematics and
science with emphasis on developing analytical, numerical, graphical and verbal
skills as required.
II. Course Objectives
A. Examine the definition of a function and investigate the implications of this
concept
B. Explore graphs of functions of the form y = f(x) = x^p
C. Create new functions from existing functions
D. Graph and analyze exponential and logarithmic functions and solve related
equations
E. Graph and analyze polynomial functions and solve related equations and
inequalities
F. Graph and analyze rational functions and solve related equations and
inequalities
G. Examine the logic of conditional and bi-conditional statements as they appear
in mathematical
statements
III. Essential Student Materials
Graphing Calculator or computer software
IV. Essential College Facilities
None
V. Expanded Description: Content and Form
A. Examine the definition of a function and investigate the implications of this
concept
1. Define a function and explore its representations graphically, numerically,
algebraically, and
verbally
2. Investigate linear functions
a. Graphs and equations of linear functions
b. Perpendicular and parallel lines
c. Interpret slope as rate of change
d. Investigate applications such as, but not limited to
1. Linear economic models
2. Depreciation
3. Investigate quadratic functions
a. Graph quadratic functions
b. Express quadratic functions in general, standard, and factored form
c. Identify relative maxima and minima as vertices
d. Investigate applications such as, but not limited to
1. Projectile motion
2. Free fall
3. Area
4. Quadratic economic models
5. Historical contributions such as contributions by the Chinese,
Babylonian, and Indian mathematicians to the solutions of quadratic
equations
4. Investigate absolute value functions
5. Investigate piecewise defined functions
6. Determine and interpret domain and range
7. Recognize one-to-one functions
8. Explore the symmetry of functions
9. Evaluate sums, differences, products and quotients of functions
10. Solve equations and inequalities involving linear, quadratic, and absolute
value functions.
B. Explore graphs of functions of the form y = f(x) = x^p
1. Draw and recognize graphs of
a. Power functions y = f(x) = x^n
b. Radical functions such as y = f(x) = x^(1/2) and y = f(x) = x^(1/3)
c. Rational functions such as y = f(x) = 1/x and y = f(x) = 1/x^2
2. Investigate relative growth of power functions as x grows large
3. Investigate applications involving direct and inverse variation, such as, but
not limited to
a. Hooke's law
b. Intensity of illumination or radio waves
c. Length and period of a pendulum
d. Gravitational force
e. Distance, constant velocity, and time
f. Area or volume
C. Create new functions from existing functions
1. Explore transformations of functions
a. Translations
b. Stretches and compressions
c. Reflections
2. Investigate composite functions
3. Develop the concept of inverse functions
a. Define inverse functions using composition
b. Find inverse functions algebraically
c. Recognize the relationship between the graph of a function and its inverse
d. Investigate the relationship between the domain and range of a function and
its inverse
e. Investigate applications involving inverse functions, such as, but not
limited to
1. Celsius and Farenheit temperature
2. Economic and business models
D. Graph and analyze exponential and logarithmic functions and solve related
equations
1. Graph logarithmic and exponential functions
2. Compare/contrast the basic properties of these transcendental functions with
those of the
algebraic functions
3. Investigate exponential growth and decay problems
4. Develop laws of logarithms
5. Identify common and natural logarithms
6. Solve exponential equations
7. Solve logarithmic equations
8. Compare the growth of exponential functions to linear and power functions.
9. Graph exponential functions on logarithmic graph paper (optional)
10. Applications such as, but not limited to
a. Compound interest
b. Exponential population models
c. Radioactive decay
d. pH
e. Intensity of sound
f. Intensity of earthquakes
g. Frequency of musical notes
h. Newton's law of cooling
i. Historical contributions such as use of exponents, and the origins of e and
logarithms
E. Graph and analyze polynomial functions and solve related equations and
inequalities
1. Investigate the Fundamental Theorem of Algebra
a. By using the relationship between zeros and factors
b. By determining the function's rational, irrational, and complex roots
c. Using synthetic division (optional)
d. Review complex numbers as necessary for this section (optional)
2. Explore the graphs of polynomial functions using the relationship between
intercepts and factors
3. Explore the behavior of graphs of polynomial functions and their relationship
to graphs of power
functions
4. Solve equations and inequalities involving polynomial functions
5. Investigate applications such as, but not limited to
a. Volume
b. Historical development of the Fundamental Theorem of Algebra by
mathematicians such as
Girard and Gauss
F. Graph and analyze rational functions and solve related equations and
inequalities
1. Examine vertical, horizontal and oblique, and other non-linear asymptotes
2. Graph functions that contain vertical, horizontal and oblique, and other
non-linear asymptotes
3. Solve equations and inequalities involving rational expressions
4. Investigate applications such as, but not limited to, average cost
G. Examine the logic of conditional and bi-conditional statements as they appear
in mathematical
statements
1. Explore the relationships between a conditional statement and its converse,
inverse, and
contrapositive.
2. Explore the use of conditional and bi-conditional statements in mathematical
statements,
definitions, and theorems.
VI. Assignments
A. Required readings from text
B. Problem-solving exercises, some including technology
VII. Methods of Instruction
Methods of instruction may include but are not limited to the following:
Lecture and visual aids
Discussion of as signed reading
Discussion and problem-solving performed in class
In-class exploration of internet sites
Quiz and examination review performed in class
Homework and extended projects
Guest speakers
Collaborative learning and small group exercises
Collaborative projects
Problem solving and exploration activities using applications software
VIII. Methods of Evaluating Objectives
A. A selection among homework, quizzes, exploratory worksheets or labs, and
group projects
B. A minimum of: (a) three one-hour written exams OR (b) one project and two
one-hour written exams.
C. Two-hour comprehensive final exam
