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 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. 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)