Analyze families of functions, including shifts, reflections, and dilations of (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer),  (quadratic), y = a^x (exponential), and y = log_ax (logarithmic).

Example: comparing the graphs of y=2^x, ,

• Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

  Example: finding the domain of or

• Identifying real-world situations corresponding to families of functions

Mathematical Investigation with Excel
This lesson uses an excel spreadsheet to model a basketball's flight. It allows you to change the angle and initial velocity of the toss and the graph changes accordingly. 

Chicago Public Schools
This is a collection of structured daily lesson plans that go from transformations to compositions of functions.

BBC Lessons
This is an interactive online lesson about general transformations of functions.

BBC Lessons
This is an interactive online lesson on the composition of functions where students can manipulate the input and output.

Getting Out of Line
In this lesson, students study nonlinear models for data in tables and in graphs. Students explore parameter changes in linear and non-linear functions.

Toothpicks and Transformations (Quadratic Functions)
Students will investigate quadratic functions using geometric toothpick designs.

Chicago Public Schools
This is a collection of structured daily lesson plans that covers rational functions.

Multiplying and Dividing Rational Functions
This is an online lesson with learning objectives detailing rational expressions.

BBC Lessons
This is an interactive online lesson on domain and range of functions.

Chicago Public Schools
This is a collection of structured daily lesson plans that go from transformations to compositions of functions.

The Absolute Truth
Students will communicate their understanding of the methods available to find and check solutions to absolute value inequalities.

Chicago Public Schools
This is a structured lesson plan that provides strategies for teaching, examples, worksheets, and assessments. Instruction on the TI-82/83 is provided, but the use of calculators is not essential. (Day 70-71)

An Introduction to Functions by Calculating, Observing Growth Rates, and Interpreting the Graphs
Students will determine the type of growth of a function to determine the best salary. Many of the common relations are represented.

Maximum Pressure on the Shuttle
Students investigate the maximum pressure on the shuttle as it goes through the atmosphere. Use data and equations to model this phenomenon in time, density, and altitude.

Basic Properties of Rational Expressions
This is a complete list of skills related to rational expressions, including examples and their solutions.

The Function Institute
This interactive applet lest students change the parameters on several classes of functions from polynomial to exponential and trigonometric.

Rational Function Graphing Applets
Examine the parameter changes in rational functions. Asymptotes are marked in some applets. All are interactive.

Interactive Quiz on the Common Relations
An applet that quizzes students on the common relations

Common Relations
This site is an explanation of common relations with examples, animations, and java applets.

The Inverse Function
A site about 1/x and other interesting rational functions.

Greatest Integer Function
This applet demonstrate the greatest integer function on the number line.
 

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