Title: Exploring Composite Functions

Grade Level: 9th-12th grade

Objective: - Understand the concept of composite functions and how to evaluate them - Apply the concept of composite functions to solve real-world problems - Develop critical thinking and problem-solving skills through hands-on activities and discussions

Materials: - Whiteboard or blackboard - Markers or chalk - Graphing calculators (optional) - Worksheets with composite function problems - Real-world scenarios for application of composite functions

Procedure:

1. Introduction (10 minutes):
   • Begin the lesson by asking students if they are familiar with the concept of functions.
   • Review the definition of a function and its notation (f(x)).
   • Explain that a composite function is formed by combining two or more functions, where the output of one function becomes the input of another function.
2. Definition and Notation (10 minutes):
   • Write the definition of a composite function on the board.
   • Explain the notation for composite functions using examples.
   • Provide a few simple examples of composite functions and ask students to evaluate them.
3. Evaluating Composite Functions (20 minutes):
   • Give students a worksheet with composite function problems.
   • Guide them through the process of evaluating composite functions step by step.
   • Encourage students to use graphing calculators to visualize the functions if available.
4. Real-World Applications (15 minutes):
   • Present real-world scenarios that can be modeled using composite functions.
   • Discuss how to identify the functions involved and set up the composite function equation.
   • Have students work in pairs or small groups to solve the problems and present their solutions to the class.
5. Practice and Reinforcement (15 minutes):
   • Provide additional practice problems for students to work on individually or in pairs.
   • Circulate the classroom to provide assistance and answer questions.
   • Review the solutions as a class and address any common misconceptions.
6. Extension Activity (10 minutes):
   • Challenge students to create their own real-world scenarios that can be modeled using composite functions.
   • Have them write the composite function equation and explain the steps to solve the problem.
   • Allow students to present their scenarios and solutions to the class.
7. Conclusion (5 minutes):
   • Summarize the key points covered in the lesson.
   • Ask students to reflect on how composite functions can be useful in solving real-world problems.
   • Encourage students to continue exploring and applying composite functions in their future math studies.

Assessment: - Evaluate students’ understanding of composite functions through their participation in class discussions and completion of the worksheet problems. - Assess their ability to apply composite functions to real-world scenarios through their presentations and extension activity.