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The Intermediate Value Theorem is sometimes used to prove that roots exist. For example,  is a continuous function. Given and , does have a root somewhere between and ? Why or why not? 

Is it possible to move from to without passing through ?   

Use the eTool below to view the graph of the functions.
Click on the link to the right to view the full version of the eTool: Calc 2-82 HW eTool (Desmos)