Worksheet: The Intermediate Value Theorem

Here, you can assess your knowledge of one of the most intuitive theorems: the intermediate value theorem. The theorem states that if L is a value between f(b) and f(a), there must be a value c where f(c) = L.

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