Let f:R→R be a function defined as : f(x) Then, f is :

Question

Let $f:R\to R$ be a function defined as :

$f(x)=\begin{cases}5,&\text{if}&x\leq1\\a+bx,&\text{if}&1<x<3\\b+5x,&\text{if}&3\leq x<5\\30,&\text{if}&x\geq5\end{cases}$

Then, $f$ is :

(1) continuous if $a=5$ and $b=5$

(2) continuous if $a=-5$ and $b=10$

(3) continuous if $a=0$ and $b=5$

(4) not continuous for any values of $a$ and $b$