Worksheet: The Intermediate Value Theorem

In this worksheet, we will practice how to apply 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?

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