Course
Outline
Institution:
Course Title: College Algebra
Course Prefix / #: Mth
111
Type of Program: Transfer
Credits: 5
Date:
Outline Developed by: Carrie Kyser
Last Review Date:
Course Description: A
transfer course designed for students preparing for trigonometry, statistics,
or calculus. AMATYC standards-based
approach utilizing the rule of four to analyze functions and their properties,
including rates of change, short- and long-run behavior, transformations and
symmetry, algebra and composition of functions, inverse functions, discrete
functions, and fitting functions to data.
Particular attention will be paid to the use of functions to model
applications and solve problems.
Length Of Course: 52 lecture hours
Grading Criteria: Letter
grade or Pass / No Pass
Prerequisites: Required: MTH 095 (C or
better) or appropriate score on the Math Placement Exam.
Recommended: Placement in
RD 115 and WR 121.
Required Material: Functions
Modeling Change: A Preparation for
Calculus, 2/e by Connally, Hughes-Hallett, Gleason, et al.
© 2004; John Wiley & Sons, Inc.
A
graphing calculator is also required (the department recommends the TI-83
Plus).
Course Objectives: This
course will foster an understanding of functions and their properties,
including rates of change, short- and long-run behavior, transformations and
symmetry, algebra and composition of functions, inverse functions, discrete
functions, and fitting functions to data. Particular attention will be paid to the use
of functions to model applications and solve problems.
Student Learning The
student will be able to:
Outcomes:
·
Define and
identify functions using each method from the rule of four.
·
Read and write function notation as a means of communication.
·
Compute and
interpret the average rate of change of a function over an interval.
·
Determine the
short-run behavior of a function.
·
Determine the
long-run behavior of a function.
·
Construct linear
functions to model applications.
·
Fit linear
functions to data sets.
·
Determine an
appropriate domain and range for a function.
·
Read and write
formulas for, and model applications using piecewise-defined functions.
·
Determine and
describe the concavity of a function.
·
Define and
identify an exponential function.
·
Construct
exponential functions to model applications.
·
Fit exponential
functions to data sets.
·
Use the natural
exponential function to model applications.
·
Define and
identify a logarithmic function.
·
Construct
logarithmic functions to model applications.
·
Fit logarithmic
functions to data sets.
·
Use the natural
logarithmic function to model applications.
·
Use the properties
of logarithms to solve equations.
·
Identify rigid
transformations of elementary functions.
·
Identify
non-rigid transformations of elementary functions.
·
Determine
symmetries of a function.
·
Define and
compute the composition of functions.
·
Perform the
algebra associated with the composition of functions.
·
Determine if a
function is invertible.
·
Find the inverse
of an invertible function.
·
Compare the
domain and range of a function with those of its inverse.
·
Define and
identify polynomial functions.
·
Use polynomial
functions to model applications.
·
Define and
identify rational functions.
·
Use rational
functions to model applications
·
Compare and
contrast linear, exponential, logarithmic, polynomial, and rational functions.
·
Define and
identify discrete functions.
·
Compare and
contrast arithmetic and geometric sequences.
·
Define and
identify series.
·
Compute the sum
of an arithmetic series.
·
Compute the sum
of a finite geometric series.
·
Determine when
an infinite geometric series converges.
·
Compute the sum
of a convergent infinite geometric series.
·
Model and solve
applications using sequences and series.
·
Demonstrate
rigorous and analytical thinking by reading, writing, and utilizing the
technical and logical language and symbolism necessary to do mathematics and to
solve problems effectively and efficiently.
·
Work effectively
as a team member to engage in problem solving.
Major Topic Outline: Linear
Functions
Function
notation, rate of change, formulas for and geometry of linear functions.
Properties of Functions
Domain
and range, piecewise-defined functions, function inverses, composition, concavity.
Exponential and Logarithmic Functions
Comparison with linear, properties of these functions
and their graphs, solving exponential equations, modeling.
Function Transformations
Shifts, reflections, symmetry.
Polynomial and Rational Functions
Comparison with linear, properties of these functions
and their graphs, solving equations, modeling.
Sequences and Series
Sequences; arithmetic, finite geometric and infinite
geometric series.
Suggested timeline: CLASS HOURS TOPIC
7 Linear Functions
7 Properties of
Functions
10 Exponential and
Logarithmic Functions
7 Function
Transformations
7 Polynomial and
Rational Functions
7 Sequences and Series
7 Assessments
/ Final Exam
52