Mathematical Analysis (Honors)
Unit 4: Polynomial Functions
In this unit, students build on their understanding of quadratic functions to explore polynomial functions. Students build new polynomial functions using the arithmetic operations of addition, subtraction, multiplication, and composition. Students analyze key features of graphs of polynomial functions including domain and range, zeros, local extrema, intervals of increasing and decreasing, and concavity. Students make connections between end behavior, the leading coefficient, and the degree, and then graph polynomial functions based on these key features. Students compare properties of two functions using multiple representations, such as, a graph, table of values, and verbal description of a realworld context. They solve polynomial equations in context using similar representations. Students find all roots of a polynomial function using algebraic methods and use them to sketch the graph.
Students will:
Interpret functions that arise in applications in terms of a context.
F.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and concavity.
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
PC.S.A.5
Use the binomial theorem to expand a binomial.
PC.S.A.6
Solve problems involving binomial distributions.
Build and interpret functions that model relationships between two quantities.
PC.AF.A.4
Perform algebraic operations on functions and sketch the resulting graph.
PC.AF.A.5
Compose functions. Verify by composition that one function is the inverse of another.
Apply understanding of polynomial functions to solve realworld problems.
MA.PF.A.1
Find all rational, irrational, and complex zeros of a polynomial using algebraic methods.
MA.PF.A.2
Use polynomial functions to model and solve realworld problems.
Interpret functions that arise in applications in terms of a context.
F.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and concavity.
 Check for Understanding: Graphs of Polynomials
 Review/Rewind: Graphs of Polynomials
 Enrichment Tasks: Graphs of Polynomial
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
 Check for Understanding: Intervals
 Review/Rewind: Zeros and Their Graphs  Intervals
 Enrichment Tasks: Graphing Polynomials
PC.S.A.5
Use the binomial theorem to expand a binomial.
 Check for Understanding: Expand
 Review/Rewind: Intro to the Binomial Theorem
 Enrichment Tasks: Powers of 11
PC.S.A.6
Solve problems involving binomial distributions.
Build and interpret functions that model relationships between two quantities.
PC.AF.A.4
Perform algebraic operations on functions and sketch the resulting graph.
 Check for Understanding: Add Expressions  Multiply Expressions
 Review/Rewind: Combining Functions  Multiplying and Dividing Functions
 Enrichment Tasks: A Sum of Functions
PC.AF.A.5
Compose functions. Verify by composition that one function is the inverse of another.
 Check for Understanding: Evaluate Composite Functions  From Graphs  Compose Functions
 Review/Rewind: Intro to Composing Functions  Composing Functions
 Enrichment Tasks: Building Functions
Apply understanding of polynomial functions to solve realworld problems.
MA.PF.A.1
Find all rational, irrational, and complex zeros of a polynomial using algebraic methods.
 Check for Understanding: Find zeros
 Review/Rewind: Zeros and Their Graphs
 Enrichment Tasks: Solving Polynomial Equations
MA.PF.A.2
Use polynomial functions to model and solve realworld problems.
 Review/Rewind: Total Value of Bills
 Enrichment Tasks: College Fund
What are some signs of student mastery?

Tools & Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! 