What This Document Is
This is an activity sheet designed to reinforce core concepts from your Calculus (MATH 220) course at the University of Illinois at Urbana-Champaign. It focuses on the practical application of functions, particularly linear and exponential models, and builds a foundation for understanding related mathematical principles. This resource is intended to be worked through actively, providing opportunities to solidify your understanding through problem-solving.
Why This Document Matters
This activity sheet is ideal for students looking to strengthen their grasp of function behavior and modeling. It’s particularly helpful when you’re transitioning from theoretical knowledge to practical application, and is best used alongside your lecture notes and textbook. Working through these types of exercises will build confidence and prepare you for more complex topics later in the course, and will be a valuable resource when preparing for assessments.
Topics Covered
* Distinguishing between linear and exponential functions
* Interpreting the components of linear functions (slope, y-intercept, x-intercept)
* Analyzing and sketching exponential functions
* Determining exponential function formulas from given data points
* Modeling real-world scenarios with exponential functions (e.g., bacterial growth)
* Introduction to inverse functions and logarithms
* Solving exponential and logarithmic equations
* Domain of functions
What This Document Provides
* A series of targeted practice problems designed to test your understanding of key concepts.
* Opportunities to visualize functions through sketching and graphical analysis.
* Exercises that require you to translate real-world situations into mathematical models.
* A bonus section introducing concepts related to inverse functions and logarithms, preparing you for future coursework.
* A framework for developing problem-solving skills in the context of linear and exponential functions.
