TRANSFORM TWICE—FUNCTION COMPOSITION

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 