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
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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
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#7
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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
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5.
#8
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Livescribe recording (see website)
Text Section 5.5
Google Form!
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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:
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#10
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Text section 5.9
Date:
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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
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Increase
Decrease
Positive
Negative