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Algebra 2: Unit 1 Families of Functions
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by Christine Koerner 3 years, 3 months ago
Big Idea 1: Operations on functions can be represented with both algebraic and graphical models.


Lessons and Additional Activities
Big Idea 1 Lessons 13 Overview (includes links to teacher notes and student activities)

Evidence of Understanding
Recognize and perform arithmetic operations on polynomials and rational expressions.
Simplify polynomials expressions properly.
 Make generalizations about how to simplify polynomials. (Division restricted to nonreducible forms.)
Recognize when a rational expression is not in simplest form and simplify it properly.

Big Idea 2: Families of functions share similar behaviors, characteristics and properties.

OASM: A2.F.1.1, A2.F.1.3, A2.F.1.4, A2.F.1.5, A2.F.1.6, A2.F.1.7 
Lessons and Additional Activities
Big Idea 2 Lessons 13 Overview (includes links to teacher notes and student activities)
Big Idea 2, Lessons 13 Lesson Plans

Evidence of Understanding
Use end behavior and the shape of a graph to identify and compare function families.

Conjecture the effect of the leading coefficient on function families.

Notice the effect a leading coefficient has on a function by using technology to explore various functions in a family and describe the pattern.

Form conjectures and generalizations about function families based on the interval behavior of the graph.

Use the characteristics of functions to describe real world situations.

Discover and predict end behavior of function families using the shape of the graph and its rate of change.

Generalize end behaviors of specific families of functions using various means such as graphs, tables, equations, and technology.

Discover how symmetry can help identify types of function families.
Use critical points to identify and compare function families.

Locate zeros of a function from a graph or a table.

Make the connection that the zeros (xintercepts, roots) of a function can separate positive and negative intervals.

Use a variety of tools such as graphs, tables, equations, and/or technology (graphing calculator, desmos, etc.) to discover and explore the concept of zeros and positive and negative intervals.

Recognize and justify how maximum and minimum points separate the intervals where a function increases and decreases.

Determine whether maximum and minimum points are relative or absolute by using the end behavior of a function.
Use the end behavior, shape of the graph and critical points to identify and compare function families.

Create a general graph for a function family when given end behavior, shape of the graph, and critical points.

Describe and generalize function family characteristics using end behavior, shape of the graph, and critical points.

Analyze the meaning of critical points and key characteristics of a function in a real world situation.

Big Idea 3: Two functions are inverses if the function f maps x to y and the inverse of f maps y to x.

OASM: A2.F.2.2, A2.F.2.3 
Lessons and Additional Activities
Big Idea 3 Lessons 14 Overview (includes links to teacher notes and student activities)
Big Idea 3, Lessons 14 Lesson Plans

Evidence of Understanding
Determine the composition of two functions.
 Find the composition of functions graphically and algebraically.
Use the composition of two functions to prove or disprove that two functions are inverses.
Determine the inverse of a function using a graph or a table.

Recognize and verify that two functions are inverses by analyzing points on a table or graph for the function and its inverse.

Compare and contrast the shape of a function and its inverse.

Build a function’s inverse by identifying points on a function’s graph or table of values.

Explore onetooneness and the need for domain restrictions.

Verify that two functions are inverses by their graphs and the line y = x.

Explain why two functions that are inverses reflect over the line y = x.
Determine the algebraic equation for the inverse of a function and be able to apply it to real world scenarios.

Big Idea 4: Functions within the same family are made by applying transformations onto the parent function.

OASM: A2.F.1.1, A2.F.1.2 
Lessons and Additional Activities
Big Idea 4 Lessons 12 Overview (includes links to teacher notes and student activities)
Big Idea 4, Lessons 12 Lesson Plans

Evidence of Understanding
Describe transformations within a function family.

Compare functions within the same family and explain transformations from the parent function.

Develop generalizations and conjectures about how each transformation affects the original function (ie. translations, dilations, and reflections). Use technology such as graphing calculators or desmos to discover and validate your findings.

Write a verbal description and/or a formula describing each type of transformation.

Create a new function when given a parent function and transformation details.
Discover and describe how transformations affect critical points and characteristics of functions in the same family.

Generalize how each transformation affects intercepts, maximums, minimums, end behavior, asymptotes, domain and range.

Conjecture and verbally describe what is preserved with each transformation and what changes.

Include changes in orientation, rate of change, distances, etc by targeting the critical points on the original graph and comparing to the critical points on the transformed graph.

Use visuals such as technology to help explore, engage, solidify, and justify student findings.

Describe the effect transformations have on real world scenarios.

Describe how the shape and characteristics of the graph are affected or not affected.

Algebra 2: Unit 1 Families of Functions

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