Intermediate Value Theorem: Examples and Applications

Instructions:

Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

Given the values of the continuous function f(x) below, how many solutions will there be to f(x)=4.1?

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1. Consider the function below. According to the intermediate value theorem, is there a solution to f(x) = 0 for a value of x between -5 and 5?

2. Consider the function below. According to the intermediate value theorem, is there a solution to f(x) = 4 for a value of x between 4 and 7?

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About This Quiz & Worksheet

This quiz and worksheet combination will help you practice using the intermediate value theorem. Practice questions provide functions and ask you to calculate solutions.

Quiz & Worksheet Goals

Use this assessment to:

  • Calculate specific intermediate values
  • Determine the number of possible solutions for some problems
  • Identify situations in which the intermediate value theorem applies and does not apply

Skills Practiced

This assessment will help you practice the following skills:

  • Reading comprehension - ensure that you draw the most important information from the related lesson on using the intermediate value theorem
  • Making connections - understanding of the concept of continuous function
  • Problem solving - use acquired knowledge to solve intermediate value practice problems
  • Knowledge application - use your knowledge to answer questions about when the intermediate value theorem applies

Additional Learning

For more information about the intermediate value theorem, review the lesson Intermediate Value Theorem: Examples and Applications. Topics include:

  • Reviewing the intermediate value theorem
  • Graphing continuous functions
  • Using tables to determine intermediate values
  • Practice using the intermediate value theorem
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