Title: Understanding Parent Functions and Transformations in College Algebra

Objective: By the end of this lesson, students will be able to: 1. Identify and describe common parent functions. 2. Understand the concept of transformations and how they affect parent functions. 3. Apply transformations to parent functions to create new equations.

Materials: - Whiteboard or blackboard - Markers or chalk - Graphing calculators or online graphing tools - Handouts with practice problems - Rulers or straight edges

Lesson Plan:

Introduction (5 minutes): 1. Begin the lesson by asking students if they are familiar with the term “parent function” and if they can provide any examples. 2. Explain that a parent function is a basic function that serves as a template for other functions. 3. Provide examples of common parent functions, such as linear, quadratic, cubic, square root, absolute value, and exponential functions. 4. Emphasize that understanding parent functions is crucial for analyzing and transforming more complex functions.

Exploring Parent Functions (15 minutes): 1. Display the graph of a linear function (e.g., y = x) on the board. 2. Ask students to identify the key characteristics of the linear parent function, such as the slope, y-intercept, and the fact that it is a straight line. 3. Repeat this process with other parent functions, encouraging students to identify their unique features. 4. Discuss the domain and range of each parent function and how they relate to the graph.

Transformations of Parent Functions (20 minutes): 1. Introduce the concept of transformations by explaining that they modify the shape, position, or size of a parent function. 2. Display the graph of a basic quadratic function (e.g., y = x^2) on the board. 3. Discuss the different types of transformations, such as translations, reflections, stretches, and compressions. 4. Demonstrate how to apply each transformation to the quadratic parent function, one at a time, using specific examples. 5. Encourage students to take notes and ask questions during the demonstration.

Practice Problems (15 minutes): 1. Distribute handouts with practice problems involving transformations of parent functions. 2. Instruct students to work individually or in pairs to solve the problems. 3. Circulate the classroom to provide assistance and answer any questions. 4. After the allotted time, review the solutions as a class, discussing the steps and reasoning behind each transformation.

Application and Extension (10 minutes): 1. Challenge students to create their own transformed functions by combining different transformations with a given parent function. 2. Ask students to graph their functions using graphing calculators or online tools. 3. Have students share their graphs with the class and explain the transformations they applied. 4. Discuss any patterns or observations that arise from the different transformations.

Conclusion (5 minutes): 1. Summarize the main concepts covered in the lesson, including parent functions and transformations. 2. Reinforce the importance of understanding parent functions as a foundation for more complex algebraic concepts. 3. Encourage students to continue practicing and exploring transformations of parent functions on their own. 4. Provide additional resources or references for further study if available.

Note: The duration of each section can be adjusted based on the pace and needs of the students.