Intermediate Value Theorem: Definition


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question 1 of 3

According to the intermediate value theorem, if you have a function where f(4) = 5 and f(6) = 3, there will be at least one point x between 4 and 6 where f(x) = 4.

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Given y below and the intermediate value theorem, how many times will y = 0 between x = 0 and x = π?

(Hint: Work in radians since one of the parameters for x is π.)

2. I have a function where f(1) = 0 and f(4) = 3. Why might there not be an x between 1 and 4 such that f(x) = 1?

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About This Quiz & Worksheet

Check your understanding of the intermediate value theorem with this quiz and worksheet combo. Use the practice questions to calculate and graph intermediate values.

Quiz & Worksheet Goals

Use this quiz to test your ability to:

  • Determine intermediate values in a function
  • Interpret graphical representations of functions
  • Apply the intermediate value theorem

Skills Practiced

This assessment will test the following skills:

  • Reading comprehension - ensure that you draw the most important information from the related lesson on the intermediate value theorem
  • Making connections - understanding of the concept of continuous line
  • Problem solving - use acquired knowledge to solve intermediate value theorem practice problems
  • Information recall - access the knowledge you've gained regarding intermediate values

Additional Learning

For more information about intermediate value theorem, review the lesson Intermediate Value Theorem: Definition. This lesson covers:

  • Defining intermediate value theorem
  • Comparing continuous lines with noncontinuous lines