Question

How can you tell if a piecewise-defined function is continuous at 0?

Answer 1

that will depend on the function used BEFORE 0 and AFTER 0
do you have any specifics?

Answer 2

www.mathforum.org/library/drmath/view/53745.html

Answer 3

\[f(x)=\begin{cases}g(x)&\text{for }x<0\\h(x)&\text{for }x\ge0\end{cases}\]
\(f(x)\) is continuous at \(x=0\) if
\[\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(x)\]
or equivalently,
\[\lim_{x\to0^-}g(x)=\lim_{x\to0^+}h(x)\]