Is it true that a continuous function that is never zero on an interval never changes sign on thatinterval? Give reasons for your answer.

Choose an answer below:

No. By the Intermediate ValueTheorem, a function could change sign without equaling zero.

No. If the function iscontinuous, it cannot change sign.

Yes. If the function is definedpiecewise, it may change signs without equaling zero.

Yes. By the Intermediate ValueTheorem, if a function changedsign, its value was zero at some point.