The Intermediate Value Theorem

This activity asks students to speculate the existence of roots based on graphs of functions. This is intended as a first exposure to the ideas of the intermediate value theorem and to provide fodder for classroom conversation about important ideas behind the theorem, including:

1. The “continuous” condition is essential (though very often overlooked by students).
2. The intermediate value theorem is silent on where there are NOT roots, but speaks to where there ARE roots (given the right conditions).

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