- Outline the three criteria a function must meet to be continuous at a specific point
- Explain the different types of breaks a function can have that make it not continuous
- Explain what it means for a function to be continuous over a range of values
- Explain the rule for calculating limits of functions that are combined
- Show how a continuous function reaches every value between its start and end points using the Intermediate Value Theorem
Continuity
Understanding continuity and discontinuities is crucial in the study of functions and their behavior. These concepts play a vital role in various fields, from pure mathematics to real-world applications in physics, engineering, and economics. In this activity, you’ll explore different types of functions and their continuity properties, identify various forms of discontinuities, and apply these concepts to specific examples. By working through these questions, you’ll deepen your understanding of how functions behave across their domains and sharpen your ability to analyze and classify discontinuities.