Question 987296
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If the function is continuous over *[tex \Large -2\ \leq\ x\ \leq \infty], then -2, 0, and 3.


But the significantly more correct answer is that it may not have any zeros.


Consider the function:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \left\{\begin{array}{lcr}-1&\text{if}&x\ <\ -2\\1&\text{if}&-2\ <\ x\ <\ 0\\-1&\text{if}&0\ <\ x\ <\ 3\\1&\text{if}&3\ <\ x\end{array}]


Which is positive on the given intervals but has no zeros at all.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \