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. No. By the Intermediate Value Theorem, a function could change sign without equaling zero. Yes. If the function is defined piecewise, it may change signs without equaling zero. No. If the function is continuous, it cannot change sign Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
No. By the Intermediate Value Theorem, a function could change sign without equaling zero.
Yes. If the function is defined piecewise, it may change signs without equaling zero.
No. If the function is continuous, it cannot change sign
Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.
Transcribed Image Text: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. No. By the Intermediate Value Theorem, a function could change sign without equaling zero. Yes. If the function is defined piecewise, it may change signs without equaling zero. No. If the function is continuous, it cannot change sign Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.
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