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Learning Math Home
Patterns, Functions, and Algebra
 
Session 8 Part A Part B Part C Homework
 
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A B C

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Notes for Session 8

Note 1: This session builds on the exploration of nonlinear functions that we began in Session 7. The activities in this session will help us develop a better understanding of cyclic functions and inverse variation.

Part A Notes:

Cyclic Functions

Part B Notes:

Inverse Proportions

Part C Notes:

Different Functions


The most famous cyclic functions are the trigonometric functions -- in particular, sine and cosine. Trigonometry is beyond the scope of this course, but we can still look at cycles as a kind of function, without worrying about closed or recursive formulas to describe them. The general method of finding formulas is to start with a sine curve and to find a way to make the curve fit the data. This is similar to finding a "line of best fit" by changing the slope and intercept on the linear equation y = x.

Materials Needed: graph paper

Review
Groups: Discuss questions about the homework. In particular, talk about Problem H2 and share the methods for solving it. Note that there is an algebraic equivalent to "undoing an exponent": taking a logarithm. (Logarithms are beyond the scope of this course, but it's important to acknowledge that such an inverse operation exists.)

Groups: Review the list of functions from the previous session. At least two more kinds of functions will be added to that list during this session.


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