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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 signYes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.

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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.
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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.

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Step 1

Is it true?

The continuous function that is never zero on an interval, never changes sign on that
interval
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The continuous function that is never zero on an interval, never changes sign on that interval

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Step 2

Answer:...

1
This function is 0 at a value which is very
Yes, it is true. Take the function f (x)
e
big that is x is infinity. This is a continuous function that is never zero on any interval and
is not changing sign on any of that interval
Also, by Intermediate Value Theorem, if the function changes sign, its value was zero at
some point
help_outline

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1 This function is 0 at a value which is very Yes, it is true. Take the function f (x) e big that is x is infinity. This is a continuous function that is never zero on any interval and is not changing sign on any of that interval Also, by Intermediate Value Theorem, if the function changes sign, its value was zero at some point

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