Show the zero exists by the Intermediate Value Theorem

The video tutorial explores the concept of continuity in polynomials and introduces the intermediate value theorem. It explains how the theorem can be used to determine the existence of zeros in polynomial functions. Through an example, the video demonstrates evaluating a polynomial function over an interval to find a zero, using both algebraic and graphical approaches. The lesson concludes by confirming the theorem's application through graphing technology.

What is the significance of the Intermediate Value Theorem in relation to continuous functions?

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Explain how the continuity of a polynomial function affects the existence of zeros within a given interval.

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Describe the conditions under which the Intermediate Value Theorem can be applied.

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How can you graphically determine the existence of a zero for a polynomial function?

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In the example provided, what values were evaluated to demonstrate the existence of a zero between the interval 2 and 3?

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What does it mean for a function to be continuous, and how does this relate to the Intermediate Value Theorem?

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What conclusion can be drawn about the value C in relation to the continuous function discussed?

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