Mathematics

Problem

Which one of the following functions is continuous throughout the closed interval

[0,3]

? a)

s(x)=\begin{cases} \sin x, & 0\le x\le \dfrac{\pi}{2},\\ 2, & \dfrac{\pi}{2}< x\le3. \end{cases}

p(x)=\begin{cases} x^{2}, & 0\le x<2,\\ 4, & x=2,\\ x+2, & 2< x\le3. \end{cases}

p_{1}(x)=\begin{cases} x^{2}, & 0\le x<2,\\ 5, & x=2,\\ x+2, & 2< x\le3. \end{cases}

q(x)=\begin{cases} x, & 0\le x<1,\\ 3, & x=1,\\ x^{2}, & 1< x\le3. \end{cases}