Lesson Plan-Module 1

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Module 1 – Relations & Functions

By completing this module, students should be able to do the following.

 Know the different representations of a function: set of ordered pairs, diagram, graph, equation.

 Find x- and y-intercepts.

 Determine symmetry of a function.

 Identify the domain and range of a function.

 Find and simplify function values, i.e. the difference quotient.  Analyze and graph piecewise defined function.

 Find the domain of a polynomial, radical, and/or rational function.  Perform arithmetic on functions.

 Find the domain of a function resulting from arithmetic operations.  Build and analyze real world functions.

 Solve application problems, including economic functions: price-demand, revenue, cost, or profit.

 Graph common functions.

o identity function:

y



x

o square function:

y



x

2

o square root function:

y



x

o cube function:

y



x

3

o cube root function:

y



3

x

o absolute value function:

y



x

o reciprocal function: y 1 x



o reciprocal square function: y 1₂ x

 .

 Determine if a function is even, odd, neither, or both.  From the graph of a function, determine

o where the function is increasing, decreasing, or constant;

o local maxima and local minima;

o absolute maximum and absolute minimum.

 Sketch the graph of a function through transformations of the graph of a given function. Transformations include shifting, reflecting, scaling, or a combination of these.

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To get to a section in this document more easily, click on the section title:

Section 1.2 Section 1.3 Section 1.4 Section 1.5

Graphs of Common Functions Section 1.6

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Module 1 Assignments

These assignments are in addition to homework, quizzes, and worksheets. Assignments may be submitted online through Canvas, preferably in pdf format to simplify grading. Assignments should be completed individually by students. In-class collaboration or instructor assistance may be helpful, as time allows.

Orientation Assignment

When?

The orientation assignment should be completed before students begin coursework.

Why?

By completing this assignment, students acknowledge that they have the necessary background and tools for completing the course. They verify their understanding of the structure and requirements of the course. This also provides a “practice run” at submitting an assignment in pdf format through Canvas.

How?

Students complete the form that has been posted in Module 1 on the Canvas site, and then submit this completed form in pdf format through the Canvas course site.

Graphing Transformations Assignment

When?

The Graphing Transformations Assignment should be completed after Section 1.7.

Why?

This assignment provides practice with transforming graphs of functions. From identifying the resulting equation after transformations of

f x

 



x

2 to sketching

transformations of the graph of a piecewise function, students will improve their understanding of and skills with graphing transformations.

How?

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Module 1 In-Class Projects

Projects are to be completed during class by pairs or groups of students.

Fundraiser Project – Part 1

When?

The first part of the Fundraiser Project should be assigned after Section 1.3.

Why?

This part of the project provides a real life application of symmetry. Additionally, students will test their understanding of even/odd functions.

How?

The introduction to the Fundraiser Project can be played before beginning the project in class.

Each group of students will decide on a fundraising cause and will then design a t-shirt that corresponds to their fundraising cause. The t-shirt design should demonstrate symmetry about the x-axis, y-axis, origin, or all three. Groups will present their designs to the class and discuss type of symmetry along with whether that symmetry is even, odd, or neither.

Fundraiser Project – Part 2

When?

The second part of the Fundraiser Project should be assigned in correspondence with Section 1.5.

Why?

This part of the project introduces a real world application of economic functions and function arithmetic that will contribute to understanding of concepts in sections 1.4 and 1.5.

How?

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1. There is a one-time fee of $50 (can be changed by instructor) for the printer to set the t-shirt design.

2. The cost of each blank t-shirt will be $3 (can be changed by instructor).

3. The cost of applying the design to each t-shirt will be $6 (can be changed by instructor).

Each group then presents their results to the class. Presentations should include:

1. The fundraising cause and goal (amount of money to be raised). 2. The t-shirt design.

3. The price of the shirts to customers.

4. Answer to the question “How many t-shirts must be sold to break even?” 5. Answer to the question “How many t-shirts must be sold to meet your

fundraising goal?”

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Lesson Plan Module 1 – Section 1.2:

Relations

Objectives:

• sketch the graph of a relation by plotting points • find x- and y-intercepts

• determine symmetry

Pre Work (outside of class):

 Complete Orientation Assignment

 Read Section 1.2 (Open Resource textbook)  Watch Section 1.2 Videos (Canvas)

o Relations – Definitions and Graphing

o Relations – Finding Intercepts

o Relations – Determining Symmetry  Complete Try On Your Own problems from videos  Complete Homework 1.2-A (Web Assign)

*

In-Class:

 Allow a few minutes for questions.

 Working in pairs, students may be assigned various problems that correspond to objectives.

Post Work (outside of class):

 Complete Homework 1.2-B (Web Assign)

**

 Take Quiz 1.2 (Canvas)

 Optional - Students can try Checkpoint Quiz 1.2 and view the video to see if they worked the problem correctly.

*

This is assignment S/Z Homework 1.2_A (3469760) in WebAssign.

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Lesson Plan Module 1 – Section 1.3:

Introduction to Functions

Objectives:

• know the definition of a function

• determine if a given relation is a function using definition, equation, or graph • identify the domain and range of a function from either definition or graph

o Functions – Definition and Vertical Line Test

o Functions – Domain and Range



Complete Try On Your Own problems from videos



Complete Homework 1.3-A(Web Assign)

*

In-Class:

 Working in groups, students complete Part 1 of the Fundraiser Project.

**

*

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Lesson Plan Module 1 – Section 1.4:

Function Notation

Objectives:

• determine a function that performs ordered arithmetic operations on a variable • find and simplify function values

• analyze a piecewise defined function

• find the domain of a polynomial, radical, and/or rational function

 Read Section 1.4 (Open Resource textbook)  Watch Section 1.4 Video (Canvas)

o Functions – Definitions and Notations

o Functions – Finding Values

o Functions – Finding Domain from an Equation  Complete Try On Your Own problems from videos  Complete Homework 1.4-A (Web Assign)

*

In-Class:

**

*

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Lesson Plan Module 1 – Section 1.5:

Function Arithmetic

Objectives:

• perform arithmetic on functions

• find the domain of a function resulting from arithmetic operations • find and simplify a difference quotient for a given function

• solve application problems, including economic functions: price-demand, revenue, cost, and profit

Pre Work (outside of class):

o Functions – Arithmetic

o Functions – Difference Quotient

o Functions – Economic Applications  Complete Try On Your Own problems from videos  Complete Homework 1.5-A (Web Assign)

*

In-Class:

 Working in groups, students complete Part 2 of the Fundraiser Project.

Post Work (outside of class):

**

*

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Lesson Plan Module 1 – Graphs of Common

Functions (not in textbook)

Objectives:

 Graph identity function:

y



x

.  Graph square function:

y



x

2.  Graph square root function:

y



x

.  Graph cube function: 3

y



x

.  Graph cube root function:

y



3

x

.  Graph absolute value function:

y



x

.

 Graph reciprocal function:

y

1

x



.

 Graph reciprocal square function:

y

1

₂

x



.

Pre Work (outside of class):

 Watch Graphs of Common Functions Video (Canvas)  Complete Try On Your Own problem from video

In-Class:

 Working in pairs, students may practice graphing common functions. This can be extended to a competition between pairs for speed or accuracy in graphing all eight common functions.

Post Work (outside of class):

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Lesson Plan Module 1 – Section 1.6: Graphs

of Functions

Objectives:



graph piecewise defined functions



determine if a function is even, odd, neither, or both



determine from a graph

o

the intervals where a function is increasing, decreasing, or constant

o

local maxima and minima

o

absolute maximum and minimum

o Functions – Piecewise Graphs

o Functions – Even and Odd

o Functions – Graph and Behavior

 Complete Try On Your Own problems from videos  Complete Homework 1.6-A (Web Assign)

*

In-Class:

Post Work (outside of class):

**

*

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Lesson Plan Module 1 – Section 1.7:

Transformations

Objectives:

• sketch the graph of a function through transformations of the graph of a given function: transformations include shifting, reflecting, scaling, or combination of these

• find the function resulting from a sequence of transformations on a given function

Pre Work (outside of class):

o Functions – Transformations of Graphs I

o Functions – Transformations of Graphs II

o Functions – Transformation of Graphs III  Complete Try On Your Own problems from videos  Complete Homework 1.7-A (Web Assign)

*

In-Class:

 Students may begin working on Graphing Transformations Assignment.

Post Work (outside of class):

**

 Complete Graphing Transformations Assignment.  Complete Module 1 Worksheet.

*

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Review - Module 1 Worksheet

The worksheet is to be completed at the end of the module and will be helpful to students in reviewing content and preparing for exams. Grading of worksheets is suggested to encourage completion although grading time can be kept to a minimum since the answer key is included with each worksheet. Worksheets should be completed individually by students and may be submitted online through Canvas in pdf format. In-class collaboration or instructor assistance may be helpful, as time allows.