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Worksheet: The Intermediate Value Theorem

Q1:

The function satisfies and . But there is no between and 1 where . Why does this not violate the intermediate value theorem?

  • Abecause the intermediate value theorem only applies on the interval
  • Bbecause the intermediate value theorem only applies to cases where , not
  • Cbecause the function is not defined on the entire interval
  • Dbecause the function is not continuous over its domain
  • Ebecause the intermediate value theorem only applies to polynomial functions

Q2:

The figure shows the graph of the function on the interval together with the dashed line .

and , but anywhere on . Why does this not violate the intermediate value theorem?

  • Abecause the intermediate value theorem only applies to functions with at some value
  • Bbecause the intermediate value theorem only applies to polynomial functions
  • Cbecause the function is not continuous at
  • Dbecause the intermediate value theorem only applies to cases where not where
  • Ebecause the function is not defined on the entire interval