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TRANSFORM TWICE—FUNCTION COMPOSITION

Grades: 7‒11

In Geometric Functions activities students create, manipulate, and experience function concepts by treating geometric transformations as functions with points as their variables.

In this activity students create and describe two functions, compose them by merging the independent variable of the second function to the dependent variable of the first, and use function notation to label the resulting variables. They describe the behavior of the composed function and predict the range for restricted domains of different shapes.

OBJECTIVES 

In this activity students will:

  • Construct two functions, name them using function notation, vary the independent variables, and observe and describe the behavior of the dependent variables.
  • Merge the input of one function to the output of the other.
  • Describe the composed function using function notation.
  • Describe the relative rate of change of the variables of the composed function by direct observation, and explain the result in terms of the original functions.
  • For a given domain, predict the range (including its location, orientation, shape and size) and identify the range as being similar and/or congruent to the domain.

COMMON CORE CONNECTIONS 
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure; (8) Look for and express regularity in repeated reasoning.

Content Standards

8.F1,2; 8.G1; F-IF1,2,9; G-CO2; G-SRT1

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-nc-sa/3.0/. If you adapt and/or share this activity, you must attribute it to "KCP Technologies, a McGraw-Hill Education Company." You may distribute it only non-commercially under the same or similar license.


This material is based upon work supported by the National Science Foundation under KCP Technologies Award ID 0918733, with grant period September 1, 2009 through August 31, 2013. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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