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Henrico County Public Schools, Virginia

 
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Module - Exploring Polynomial Functions
Lesson 1 - Polynomial Functions
8 - Inverse Functions and Relations
Objective

The student will be able to evaluate polynomial functions and identify general shapes of the graphs of polynomial functions.

Area of an Irregular Polygon

Jimmy went for a 4 hour bike ride on Saturday morning. The graph below displays his speed at different times of the ride. Find the area of the polygon formed by this graph. Hint: You will need to divide this polygon into smaller sections that you know how to find the area of. There are many ways to do this, but if you need help, try checking the check boxes for suggested sections. Use the tools at the top of the window to draw in your own sections. On your own paper, show your work and find the total area of the irregular polygon.


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SOL

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AII.6 -   The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.

AII.7 c, d, e, & f - The student will investigate and analyze functions algebraically and graphically. Key concepts include
a)   domain and range, including limited and discontinuous domains and ranges;
b)   zeros;
c)   x- and y-intercepts;
d)   intervals in which a function is increasing or decreasing;
e)   asymptotes;
f)   end behavior;
g)   inverse of a function; and
h)   composition of multiple functions.
Graphing calculators will be used as a tool to assist in investigation of functions.

Common Core Standards

Warm-up
  1. ExamView: Solving Quadratic Systems Review
Lessons
  1. Notes: Domain and Range (ppt)
  2. Notes: Families of Graphs (ppt) *New for 2009*
  3. Teacher Notes: Families of Functions Lesson (pdf) *New for 2009*
  4. Notes: Functions (ppt) *New for 2009*
  5. Notes: Asymptotes (ppt) *New for 2009
Videos

 

Explore Learning

 

Geogebra

 

Internet Sites
  1. Notes: Domain and Range notes from GMU
  2. Notes: Functions notes from maths online
  3. Notes: Functions versus Relations notes from Purplemath.com
  4. Notes: Vertical and Horizontal Asymptotes at Purplemath.com *New for 2009*
  5. Notes: End Behavior of Polynomials at Purplemath.com *New for 2009*
  6. Notes: End Behavior of Polynomials at Virtual Math Lab *New for 2009*
  7. Activity: Cubic Function Activity from Explorelearning.com
  8. Activity: Absolute Value Activity from Explorelearning.com
  9. Video Tutor - Polynomails
Tasks

 

Practice
  1. Classwork: Polynomial Functions Worksheet (pdf)
  2. Homework: Polynomial Functions Worksheet #1-12 (pdf)
  3. Homework: Asymptotes (pdf) *New for 2009*
Assessment
  1. ExamView: Polynomial Functions Quiz
  2. ExamView: Asymptotes Quiz *New for 2009*
Other

 

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