THE NATURE OF GRAPHS

• Symmetry and Coordinate Graphs
• Even and Odd Functions -- Go to section 3
• A tutorial on even and odd functions
• Even and Odd Functions
• Explore an even function -- use your calculator
• Explore an odd function-- use your calculator
• Comparing even and odd function -- use your calculator
• Another visualization of an odd function -- use your calculator
• A quiz on even and odd functions
• Symmetry plotter
  
• Families of Graphs
• Exploring reflections
• Mystery Graphs using reflections
• Reflections of a Quadratic Function applet
• Reflections of a Linear Function applet
• Geometric transformations of functions
• Visualizing transformations of functions
• Function transformation plotter
  
• Quiz on transformations of functions
• Translations of Graphs
• Mystery Graphs using translations
• Scaled and Shifted Graphs -- scroll down to read the information -- good problems under Exercises for this Topic
• Translations and Shifts of Graphs
• Graphs of Nonlinear Inequalities
• Graph Absolute Value of a Linear Function applet
• Absolute Value of a Quadratic Function applet
• Inverse Functions
• Good discussion & visualization -- use your calculator
• Exploring Inverses -- use your calculator
• Guess the inverse function
• Inverse Functions (click on inverse functions)
• Problems on finding the inverse of a function
• Use the horizontal line test to test for functions; also find an inverse of a function
• Inverse functions applet
• Continuity and End Behavior
  
• Continuity
• More on Continuity and the Intermediate Value Theorem
• Intermediate Value Theorem
• Intermediate Value Theorem (slide show)
• Explore the Intermediate Value Theorem
• Definition of continuous functions
• What makes a function continuous? (slide show)
• Continuity applet
• Problems on the importance of continuity
• Continuity of functions in one variable
• Discussion and visualization of continuity
• A function continuous at all irrationals, discontinuous at all rationals.
• A function that is continuous at only one point (salt & pepper functions)
• Critical Points and Extrema
• Increasing/Decreasing Functions
• Polynomials Functions of Higher Degree
• Graphing polynomials
• Graphing polynomials -- (Work problems on all levels under Graphing Polynomials)
• Two problems about graphing functions
• Basics concerning polynomial functions
• Comparing graphs -- use your calculator
• More comparisons -- use your calculator
• Graphing 4th degree polynomial applet
• Maximum or Minimum Values of Polynomial Functions
• Some problems to try (you don't have to download his file; just work through the worksheet. There are three pages of problems.)
• Maximize Area of a Rectangle applet
• Minimize Perimeter of a Rectangle applet
• Problems
• Demonstrate the strategy for constructing a triangular sail with maximum area.
• Application Problems using Polynomial Functions
• Applied Problems using functions
• More applications to set up (Work all levels of problems on Modelling Real World Problems)
• Graphs of Rational Functions
• Basics of Rational Functions
• Exploring Graphs of Rational Functions
• Problems to graph (Work all levels of problems on Graphing Rational Functions)
• Introduction to Asymptotes
• Vertical Asymptotes
• Finding Horizontal Asymptotes, using limits
• Finding oblique asymptotes, using limits
• More on oblique asymptotes
• Tool to find asymptotes of a function
• Finding intercepts on graphs
• Direct, Inverse, and Joint Variation
• Direct Variation
• Variation Equations
• Inverse Variation
• Combinations of Functions
• Lesson on adding, subtracting, multiplying, and dividing functions
• Visualizing combining functions -- use your calculator
• Combination of functions plotter
  
• Discussion and visualization of the composition of functions
• Problems about composition of functions
• Problems -- decomposing a composed function
• Drill on writing compositions of functions
• Summaries and Review Problems: Functions & Graphs, Combinations & Inverse Functions & Scatter Plots
• Problems to try
• Review questions for composition of functions -- Go to Calculus Book I, then Functions and Geometry, then Functions, then Composition of Functions
• More review questions on inverse functions with solutions and explanations
  

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