Is it true that a continuous function that is never zero on an interval never changes sign on that interval? Give reasons for your answer. Coose the correct answer below. O No. If the function is continuous, it cannot change sign. Yes. If the function is defined piecewise, it may change signs without equaling zero. No. By the Intermediate Value Theorem, a function could change sign without equaling zero. Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.

Is it true that a continuous function that is never zero on an interval never changes sign on that interval? Give reasons for your answer. Coose the correct answer below. O No. If the function is continuous, it cannot change sign. Yes. If the function is defined piecewise, it may change signs without equaling zero. No. By the Intermediate Value Theorem, a function could change sign without equaling zero. Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.
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