# let \(f:\mathbb{R}\rightarrow\mathbb{R}\) be defined by \(f(x)=\left{\begin{array}{rcl} x^2+1,&\mbox{if}&x\leq 0\\\frac{1}{2}(x+2),&\mbox{if}&x\geq 0\end{array}\right\), then \(f\) is

let \(f:\mathbb{R}\rightarrow\mathbb{R}\) be defined by \(f(x)=\left{\begin{array}{rcl} x^2+1,&\mbox{if}&x\leq 0\\\frac{1}{2}(x+2),&\mbox{if}&x\geq 0\end{array}\right\), then \(f\) is

not continuous at \(x=0\)

not continuous on \(\mathbb{R}\)

—>> continuous on \(\mathbb{R}\)

continuous at \(x=0\)