Graphs of Functions and Systems of Equations

Precalculus will be moving beyond their introduction to functions and function notation from Algebra II and into a in-depth development of transformations. We will be applying transformations (translations, reflections, dilations, etc.) to many of the parent functions included in the image above (we will save trigonometry for the Spring!). Understanding transformations is a crucial link between the algebraic form of a function and its graphical behavior. We will spend a considerable amount of time exploring this topic and working toward mastery. You all will continue to complete the lengthy linear programming problem set and for that reason I have a great deal of information to post--I will post the homework, reference materials, and a YouTube video that goes over the basics of linear programming from the previous week on linear programming as well as the upcoming information on transformations! Enjoy.

Text Examplars:	Homework	Reference Material	Wolfram Demonstration

Upcoming Material for the next two weeks.

Text Examplars:	Homework	Reference Material

Videos on Transformations: 
Brightstorm Videos

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Algebra 2 will be moving into systems of equations through the lens of coordinate geometry.  Below is a student work example of some of the resources I will be using and what we will be exploring.  The purpose is for students to have a concrete link between their algebraic worlds and geometric worlds as well as to ground the solving of systems in the graphical world and slowly move to more abstract manipulation.

Check out this 3D Lathe that will help you visualize the creation of 3D geometric figures from the two-dimensions of the coordinate plane.
http://www.fi.uu.nl/toepassingen/00182/toepassing_wisweb.en.html

Homework                   (from the University of Houston)	Reference Material	Reference Sheet 1	Reference Sheet 2

Brightstorm Videos:
These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!

Harvard Medical School Opportunity, More Linear Programming and Linear Functions

HPREP is a free 9-week program that takes place at the Harvard Medical School campus on Longwood Ave, Boston, on Saturday mornings from 10:00AM to 2:00PM. The program will begin on November 19th, 2011 and end in early February 2012. The application, along with more information, can be found at http://sites.google.com/site/hmshprep/application-deadlines. The application is also attached to this email. Applications are due October 19, 2011 by email to HPREP@hms.harvard.edu.

From http://news.discovery.com/space/nobel-prize-physics-111004.html

The pictures above represent a few images from the work of Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess, the most recent recipients of the Nobel Prize in Physics. If you are interested in their work on the accelerating universe, here is a link to an approachable summary on the topic.  Mathematics is at the heart of their discovery and reiterates the central role of math in understanding our world.


 We have yet another short week ahead of us, but I hope that we can really engage the material and deepen our understanding of mathematics.

Algebra II will be examining linear equations within the context of functions and addressing any and all misconceptions about linear relationships.  We will spend these four days solidifying linear equations as a basis for a brief but rigorous investigation of systems of equations as well as the basis of our exploration of polynomials.
Homework is due in two weeks, October 21st.

Slides:	Classwork (from eMathInstruction):	Homework (from XYZ Custom Plus):	Linear Equations Reference Sheet

________________________________________________________________________________________ Precalculus is zeroing in on linear programming. We started our investigation with a modified version of the National Council for Teacher's of Mathematics "Dirt Bike Dilemma" and will continue to explore it over the next six days. Homework is due in two more Fridays!  A great deal of graphing and interpreting is involved so work steady and check-in with me regularly.Here is the link to the chapter from which the problem set came.
Please find the slides related to linear programming here as well and some exemplar problems to help guide you on your way.

Slides:	Text Examplars:	Homework	Reference Material

Video resources:
Brightstorm Videos on solving and graphing inequalities
Khan Academy on graphing inequalities
Youtube Video 1 on Linear Programming
Youtube Video 2 on Linear Programming
________________________________________________________________________________________ Remember, you all have ongoing Khan Academy assignments with the first installment due November 1st, and the ability to practice and get immediate feedback at TenMarks. If you have forgotten your password for TenMarks just e-mail me.