Advanced Algebra Fall 2015, Hailer Unit 3: Polynomial Functions Name (first and last) _________________________ Pd______ Livescribe recordings and other info can be found here: http://www.tamdistrict.org/Page/5861 Prepare / Review Assignment Topic and Prior to class, preview one or more of the For stamps, write assignments Topic # Stamp here…. following resources and complete the Learning Objectives Due by start of next class Google Form, if any. #1 1. 2. Text section 2.1 http://www.coolmath.com/algebra/ 15-functions (topics 1-7) Functions and Relations 1. Identify functions using graphs, tables, sets, or mapping diagrams 2. Understand and use function notation 3. Evaluate a function with a given input value or expression Handout – Evaluating Functions; AND Text 2.1, p 76-77 #9-13, 17, 19, 2124 all, 27-33 odd 1. Watch the Livescribe recordings for Graphing Absolute Value Functions (see website for links) Do the activity on pages 121-122 Read text section 2.7 Transformations of Functions: Absolute Value 1. Be able to graph the absolute value parent function and translation of the form f ( x) a | x h | k 2. Identify the vertex, (h, k), from an equation 3. Use the Vertical stretch factor, a, to graph the function Properties of Exponents 1. Evaluate Numerical Expressions 2. Use scientific notation in applications 3. Simplify Expressions 4. Compare Volumes Evaluate and Graph Polynomial functions 1. Identify Polynomial Functions 2. Evaluate by substitution 3. Determine end behavior as x gets very large or very small 4. Graph polynomial functions using a table of values Text p2.1, p78-79 #34-39 all, 42, 43, 45, 5165 odd. AND Handout: Graphing Abs. Val. Date: 10/20-21 #2 Date: 10/22-23 #3 Date: ________ 2. 3. 1. 2. 3. 1. #4 Date: ________ 2. 3. #5 1. 2. Date: ________ 3. #6 Date: ________ #7 Date: ________ 1. 2. 3. 1. 2. 3. Complete problems on page 328, fill out Google form http://www.coolmath.com/algebra/ 01-exponents Read section 5.1 in text Livescribe recording (see website), Graphing Polynomial Functions 1 Text section 5.2 http://www.coolmath.com/algebra/ 22-graphing-polynomials, topics 1-3, 9,10 Text Section 5.9 http://www.coolmath.com/algebra/ 22-graphing-polynomials, topics 4-8 Livescribe recording (see website), Graphing Polynomial Functions 2 Text Section 5.3 Livescribe recording (see website) Google form! Text sections 5.4 and 5.6 Livescribe recording (see website) Search the topic on www.khanacademy.org Analyze Graphs of Polynomial Functions 1. Understand the vocabulary of zeros, factors, solutions and Intercepts as equivalent statements 2. Identify key characteristics of polynomial graphs Operations with Functions, +, -, *, / 1. Create new functions from one or more functions 2. Create new polynomial Functions from one or more polynomial functions using +, -, * 3. Identify and use special product patterns to multiply polynomials Factor and Solve Polynomial Functions 1. Completely factor polynomial functions to find x-intercepts (find real solutions) 2. Factor the sum or difference of two cubes 3. Factor by grouping 4. 5. #8 1. 2. 3. Livescribe recording (see website) Text Section 5.5 Google Form! 1. 2. 3. Text section 5.7 Livescribe recording (see website) http://www.sosmath.com/algebra/f actor/fac04/fac04.html Search the topic on www.khanacademy.org Date: ________ #9 Date: ________ 4. #10 1. Text section 5.9 Date: ________ Use U-substitution to factor higher degree functions as quadratics Find all real and complex zeros of a function through factoring and/or graphing when not factorable. Learn Polynomial Division and Analyze the Remainder 1. Learn and use both long division and synthetic division of Polynomials 2. Use the Remainder Theorem, r=f(k) for f(x)/(x-k), where k is a constant 3. Use the Factor theorem to determine factors of f(x) Fundamental Theorem of Algebra 1. Find the number of solutions or zeros of a polynomial function 2. Find repeated solutions 3. Find all zeros of a polynomial function 4. Use zeros to write a polynomial functions, including complex and irrational roots and their conjugates 5. Use Descartes’ Rule of Signs to determine number of positive real roots, negative real roots and imaginary roots Writing Functions of Polynomials 1. Write a function given a graph 2. Write a function using finite differences Planned Quiz and Test Dates: 10/27-28 (15 points) 11/5-6 (25 Points) 11/12-13 (40 points) 11/19-20 (100 points) Vocabulary for Unit: Relations and Functions Reflection Degree Vertical Line test Piecewise Function Discrete vs. Continuous Input / Independent Variable Domain and Range Polynomial Function Output / Dependent Variable Local Max or Min End Behavior Function Notation Monomial Fundamental Theorem of Algebra Transformation Binomial Descartes’ Rule of Signs Translation Trinomial Factor Theorem Absolute value function Polynomial Rational Zero Theorem Intervals of Increase Decrease Positive Negative

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# Advanced Algebra Fall 2015, Hailer Unit 3: Polynomial Functions