Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 6: Polynomial and Rational Functions
Time Frame:
CC #
Common Core
Evidence / Assessments of learning
Instructional
Notes/Strategies
Differentiation
Student Understandings
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A.APR.2
Polynomial Functions
The Division algorithm
Remainder and Factor Theorems
The Rational Zero Test and Finding Real
Zeros
Know and apply the Remainder Theorem: For a
polynomial p(x) and a number a, the remainder on
division by x – a is p(a), so p(a) = 0 if and only if (x –
a) is a factor of p(x).
A.APR.3
Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to
construct a rough graph of the function defined by the
polynomial.
A.APR.6
Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form
q(x)+r(x)/b(x),where a(x), b(x), q(x) and r(x) are
polynomials with the degree of r(x) less than the
degree of b(x) using inspection, long division, or, for
the more complicated examples, a computer algebra
system.
F.IF.7c
Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior.
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Rational Functions
Vertical asymptotes and Holes
Graphing Rational Functions
Complex Numbers
Use the Fundamental Theorem of Algebra
Define and divide polynomials
Apply the Remainder and Factor Theorems and
make connections between remainders and
factors
 Determine the maximum number of zeros of a
polynomial
 Find all the rational zeros of a polynomial
 Factor a polynomial completely
 Recognize and describe the graphs of various
polynomial functions
 Identify the properties of general polynomial
functions
What is the procedure that is used to find real zeros of
a polynomial function?
3.3 Polynomial
Functions
and Models
3.7 The Real Zeros
of a Polynomial
Function
Math 105 12.1, 12.3, 12.4
SMART Notebook:
Polynomial Functions and
Graphs
Shmoop: Downloadable
Worksheet & Answers (see
"Links")
Analyze Math: Polynomial
Functions
Hotmath.com: End Behavior
of a Function
Illustrative Mathematics:
Zeroes and Factorization of a
General Polynomial
ck-12 Foundation: Real Zeros
of Polynomials
ck-12 Foundation: Finding
Zeros of Polynomials
Math is Fun: Polynomials:
Sums and Products of Roots
Purplemath: The Factor
Theorem
Purplemath: The Rational
Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 6: Polynomial and Rational Functions
Time Frame:
CC #
Common Core
Evidence / Assessments of learning
Instructional
Notes/Strategies
Differentiation
Roots Test
Math Bits: Geometer's
Sketchpad file for Specialty
Functions
Regents Prep: Solving and
Graphing Polynomial
Equations of Higher Degree
TI NSpire CX Activity:
Precalculus: End Behavior of
Polynomial Functions
TI NSpire CX Activity:
Precalculus: Multiplicity of
Zeros of Functions
NCTM Illuminations:
Building Connections
Polynomial Functions
F.IF.7d
Graph functions expressed symbolically and show key
features of the graph, by hand in the simple cases and
using technology for more complicated cases.
Graph rational functions, identifying zeros when
suitable factorizations are available, and showing end
behavior.
 Find the domain of a rational function
 Find intercepts, asymptotes, and holes
 Describe the end behavior of a function
 Find the number of zeros of a rational function
 find asymptotes of rational functions
Can students find horizontal and vertical asymptotes
of rational functions? Can students determine the
discontinuities of a rational function and name its
type? Can students analyze and sketch graphs of
rational functions?
3.4 Rational
Functions I
3.5 Rational
Functions II
Math 105 13.1
Math TV (Select:
Algebra>Graphing>Equations
with Rational Expressions)
Purplemath: Graphing
Rational Functions:
Introduction
Promethean Flipchart:
Rational Functions
Purplemath: Slant, or
Oblique, Asymptotes
Khan Academy: Asymptotes
of Rational Functions
TI NSpire CX Activity:
Lafayette Parish School System
Advanced Math Pre-Calculus Curriculum Map
Unit 6: Polynomial and Rational Functions
Time Frame:
CC #
Common Core
Evidence / Assessments of learning
Instructional
Notes/Strategies
Differentiation
Precalculus: Rational
Functions
TI NSpire CX Activity:
Precalculus: Exploring
Vertical Asymptotes
TI NSpire CX Activity:
Precalculus: Crossing the
Asymptote
SMART Notebook: Rational
Functions-Precalculus
Jeopardy Game
N.CN.3
N.CN.8
N.CN.9
Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex
numbers.
Extend polynomial identities to the complex numbers.
For example, rewrite x2  4 as ( x  2i)( x  2i) .
Know the Fundamental Theorem of Algebra; show
that it is true for quadratic polynomials.
 Find the conjugate of a complex number
 Simplify square roots of negative numbers
 Use the Fundamental Theorem of Algebra
How do you find the conjugate of a complex number?
rational function and name its type?
Section A.7
Complex Numbers
3.8 Complex Zeros:
Fundamental
Theorem of Algebra
Math is Fun: Fundamental
Theorem of Algebra
Education.com: Complex
Solutions of Quadratic
Equations Help (extends
beyond Quadratics)