We start with the parent functions: f(x) = x2 to f(x) = x7. My students have already been exposed to the concept of parent functions for quadratic, linear, absolute value, and rational functions. I present each one and allow time for student to make quick sketches in their notes. I mark the vertex or center of each parent graph as well as the two points one unit way. Focusing on these points gives the students a pattern to follow as well as points to accurately show all transformations, including stretches/shrinks, in future lessons.
Once we have covered all six, the students talk with their partners about any patterns they see, followed by a group discussion. I make sure to ask WHY each observed pattern is true. Then the students record a statement describing the pattern(s) including the WHY in their notes.
This leads into a discussion on end behavior for even degree functions. First we define even functions. We do a think-pair-share on functions we have already seen that are even. Next we discover/discuss end behavior of even functions. I choose not to give a formal definition yet since I want my students to develop a solid conceptual understanding. I find that students often get stuck on formal definitions and never really grasp what is being said. A formal definition can always be introduced later once students master the concept.
I have students define with their partner what the graph ends are "doing" and then share out as a whole class. Definitions should include [increasing or decreasing] behaviors for BOTH extremes of the graphs. I encourage the students to evaluate their definitions for completeness and accuracy (Math Practice 3). To wrap up the conversation, students write down their definitions including diagrams that may be helpful.
I then repeat the conversation now for the opposite [negative] even functions and again for odd functions. Each discussion should move along faster since students are building on their initial concept of end behavior.
Polynomial Functions (Algebra 2 Curriculum - Unit 5)
This bundle includes notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics:
• Operations with Monomials (exponent rules review)
• Classifying Polynomials
• Operations with Polynomials (add, subtract, multiply, divide by monomial)
• Graphing Polynomial Functions
• Identifying Key Characteristics of a Polynomial Function: domain, range, turning points (relative minimums and maximums), end behavior, increasing intervals, decreasing intervals zeros
• Zeros of a Polynomial Function, Multiplicity, Effect of Multiplicity on a Graph
• Factoring Polynomials (includes GCF, difference of squares, sum of cubes, difference of cubes, trinomials, four terms)
• Solving Polynomials by Factoring
• Dividing Polynomials (by factoring, long division, and synthetic division)
• Operations with Functions
• Compositions of Functions
• Regression (review of linear/quadratic, cubic, quartic)
NEW: Assessments are now EDITABLE! Now you can easily make multiple versions or customize to fit your needs! PowerPoint and Equation Editor (usually built in to PowerPoint) are required to edit these files. There is a folder titled "Editable Assessments" when you download. This is where you will find editable versions of each quiz and the unit test. If your Equation Editor is incompatible with mine, simply delete my equation and insert your own.
This resource is included in the following bundle(s):
Algebra 2 Curriculum
More Algebra 2 Units:
Unit 1 – Equations and Inequalities
Unit 2 – Linear Functions and Systems
Unit 3 – Parent Functions and Transformations
Unit 4 – Quadratic Equations and Complex Numbers
Unit 6 – Radical Functions
Unit 7 – Exponential and Logarithmic Functions
Unit 8 – Rational Functions
Unit 9 – Conic Sections
Unit 10 – Sequences and Series
Unit 11 – Probability and Statistics
Unit 12 – Trigonometry
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