Continuity - Worksheet 9 - 12th Grade
HardDetermine continuity and identify types of discontinuities (Hard)
27 problems · 20-25 minutes · Skills: continuity, calculus, functions
About This Worksheet
This hard-level worksheet contains 27 problems designed for 12th Grade students practicing continuity of functions. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.
Continuity is one of the most important properties a function can have — it guarantees that the function behaves predictably and that calculus tools apply. The Intermediate Value Theorem, a consequence of continuity, is a foundational existence theorem used throughout calculus to prove that solutions to equations must exist.
- State the three conditions for a function to be continuous at a point
- Classify discontinuities as removable, jump, or infinite
- Apply the Intermediate Value Theorem to guarantee the existence of roots
- Determine a constant that makes a piecewise function continuous
- Identify the type of discontinuity from the limit and function value
How to Solve: Worked Example
- Read the problem carefully.
- Identify what is being asked.
- Use what you know to find the answer.
- Check your work.
Answer Key
Frequently Asked Questions
How do I download this continuity - worksheet 9 worksheet?
Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.
How do I find worksheets at different difficulty levels?
Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.
What skills does this limits & continuity worksheet cover?
This worksheet focuses on continuity, calculus, functions. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.
Can I use this worksheet in my classroom?
Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.
How many problems are on this worksheet?
This worksheet contains 27 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.