Exploring Composition of Functions Graphically

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Exploring Composition of Functions Graphically

• Naomi Driscoll
• Channelview High School

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Introduction

• The website I chose presents the composition of
  functions from a graphical perspective.
• This lesson should help the students connect the
  algebraic and the graphical perspectives.
• I would present this lesson after having studied
  compositions algebraically.

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Agenda

• The students will use the website to complete the
  worksheet.
• The activity should take approximately ten minutes

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Overview

• The website shows the graph of each individual
  function as well as the graph of the composition
  of the two functions.

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Vocabulary

• The student should be familiar with the notation
  fog(x) f(g(x)) and
• gof(x) g(f(x))

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Algebraically

• If f(x)y
• Then gof(x)g(f(x))g(y)
• The domain for g is the range of f.

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Graphically

• Look at the graph of the first function f and
  pick a point on that graph.
• The x-coordinate of that is the same as the
  x-coordinate of the composition of the two
  functions.
• Take the y-coordinate of that point and use it as
  the x-coordinate for the second function g. Use
  the graph of g to find the corresponding
  y-coordinate which is g(f(x)).

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Summary

• On the website, the x and y-coordinates are color
  coded which helps to clarify the concept
  graphically.
• This lesson should help the students get a more
  complete understanding of function composition
• Now lets try the student worksheet.

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Where to Go to Access the Website

• http//orion.math.iastate.edu/algebra/sp/xcurrent/
  applets/composition.html