# Thread: Defining a continuous piecewise function

1. ## Defining a continuous piecewise function

I would really appreciate someone's help on a piecewise function-related question that I have. I'm wondering in the case when a piecewise function is continuous, does it matter which sub-function (in the case when there's two sub-functions) is defined as the less than or equal to sub-function? I would think that it would not matter since they are connected after all, but I just want confirmation for my reasoning is right. I attached an example in this post. Thanks

2. ## Re: Defining a continuous piecewise function

Is it clear to you that these two functions are equivalent?
$f(x)=\begin{cases}\sqrt{x} &: x\ge 1 \\ |x| &: x<1\end{cases}$ and $g(x)=\begin{cases}\sqrt{x} &: x>1 \\ |x| &: x\le 1\end{cases}$

If not surely the only question is possibly about $x=1$.
But $\displaystyle{ f(1) = {\lim _{x \to 1}}f(x) = 1 = g(1) = {\lim _{x \to 1}}g(x) }$ removes all doubt.