Functions

Course Summary: Functions

This course provides middle school students with a comprehensive understanding of functions, a foundational concept in mathematics. Through hands-on activities, real-world applications, and engaging lessons, students will learn how functions are defined, explored, and applied in various contexts. From basic operations to advanced transformations, the course equips students with essential problem-solving skills and prepares them for future mathematical studies.

Course Units:

1. Introduction to Functions

   • Explore the concept of functions, their notation, domains, ranges, and how they are represented graphically.

2. Types of Functions

   • Learn about linear, quadratic, absolute value, and exponential functions, including their properties and graphs.

3. Operations with Functions

   • Perform operations such as addition, subtraction, multiplication, and division on functions, and understand composition and inverses.

4. Transformations of Functions

   • Investigate how functions change through shifts, reflections, stretches, compressions, and combinations of transformations.

5. Applications of Functions

   • Solve real-world problems using functions, explore piecewise and step functions, and apply optimization techniques.

This course lays the groundwork for understanding the powerful role functions play in mathematics and beyond.