1 Warning
Community College of Philadelphia is a firm adherent to the
principle of academic freedom. In light of
this, faculty are not required to follow a particular approach or a particular
textbook for the courses they
teach. Most faculty, however, have more or less uniform guide lines for specific
courses, and indeed,
many use a particular textbook or approach in order to conform to area
institutions. Therefore, the
sample syllabus found here is not binding to faculty, but represents a synthesis
of what most faculty
do or aspire to do when they teach a particular course. What follows should not
be interpreted as a
prescription, but rather, as a means to help the placement of our students in
transfer institutions.
2 Cata logue Description
Functions and their applications to algebra, real numbers ,
distance and locus problems in the plane,
polynomial functions, graphs of functions, inverse functions, rational
functions , their zeros and poles .
Prerequisite: MATH 118 with a grade of C or better.
3 Allotted Time
Math 161 is a 3-credit course. Courses at Community
College of Philadelphia run for about 42 55-
minute periods. Instructors usually give three or four exams (generally lasting
at least 55minutes), and
a 2-hour long final exam.
4 Topics Outline
• The Real Line: Intervals and non- linear inequalities .
• The Coordinate Plane: Sets on the plane. The distance
formula. Circles .
• Equations and Graphs: Symmetry of Curves.
• Functions: Definitions. Natural Domain of a Function.
Even and odd functions.
• Linear Functions: Equations of lines. Equations of
parallel and normal lines.
• Quadratic Functions : Discriminant characterization of
quadratics. Translations and distortions
of parabolas .
• The Absolute Value, The Square Function , and the
Greatest Integer Function: Their canonical
graphs and transformations of their graphs.
• Arithmetic Combination of Functions: Sums, differences,
products and quotients of functions.
Characterization of the domains of arithmetic combinations of functions.
• Composition of Functions: Characterization of the domain
of the composite function. Factorization
of a function in terms of elementary functions. Graphs of compositionswith the
absolute
value function.
• Inverse Functions: Injective and Surjective Functions.
Criteria for invertibility. Graph of the inverse
function.
• Polynomial Functions: Graphs of polynomial functions
splitting in the real field.
• Finding Factors and Zeros of Polynomials: Ruffini’s
factor theorem.
• Rational Functions: Graphs of rational functions whose
numerators and denominators are polynomials
splitting on the real field.
• Other Algebraic Functions: Square root function. Cubic
root function. Combinations of these
functions.
• Complex Roots of Polynomials: Arithmetic operations with
complex numbers.
5 Competencies
1. The Student will demonstrate knowledge of the Real Line
and the Cartesian Plane by
(a) computing intersections, unions, and differences of
intervals
(b) graphing Cartesian products of intervals on the plane
(c) expressing the solution set of non-linear inequalities in interval notation
(d) expressing the sumof absolute values of linear expressions without absolute
values
2. The Student will demonstrate understanding of the
concept of a function by
(a) determining all functions froma finite set to another
finite set
(b) identifying the domain, the target set, and image of a function given a
particular function
(c) performing various algebraic operations with functions
(d) performing the composition of two ormore functions
(e) noticing how various rigid transformations and distortions affect the graph
of a function
(f ) explaining the concept of invertibility of a function and the relationship
of the graph of an
invertible function with the function
3. The Student will demonstrate knowledge of piecewise
defined functions by:
(a) Defining piecewise defined functions.
(b) Graphing piecewise defined functions.
4. The student will demonstrate an understanding of
polynomial functions by
(a) analyzing the graph of a polynomial function, its
behavior near its zeros and its end behavior.
(b) using the appropriate theorems of polynomials to factor a polynomial
function and find all
its zeros.
(c) stating the Fundamental Theoremof Algebra.(d) using appropriate rules or
theorems to determine the existence, location and classification
of the zeros of a polynomial function.
(e) using the appropriate theorems of polynomials to build a polynomial function
given its zeros
or its graph.
(f ) graphing polynomial functions.
5. The student will demonstrate an understanding of
rational functions by
(a) graphing rational functionswhich have asymptotes
including vertical,horizontal and oblique.
(b) analyzing the behavior of the graph of a rational function about a point of
discontinuity.
6. The student will explore other algebraic functions by
(a) graphing transformations of a function given its graph
or its equation.
(b) graphing piecewise functions that include nonlinear pieces.
(c) constructing and graphing functions that model real life applications and
solving related
problems.
