Let f : R → R be a function defined as:

$f(x)=\left\{\begin{array}{ccc}5 & \text { if } & x \leq 1 \\ a+b x & \text { if } & 1

$f(1)=5, \quad f\left(1^{-}\right)=5, \quad f\left(1^{+}\right)=a+b$

$\mathrm{f}\left(3^{-}\right)=\mathrm{a}+3 \mathrm{~b}, \mathrm{f}(3)=\mathrm{b}+15, \mathrm{f}\left(3^{+}\right)=\mathrm{b}+15$

$\mathrm{f}\left(5^{-}\right)=\mathrm{b}+25 ; \mathrm{f}(5)=30 \quad \mathrm{f}\left(5^{+}\right)=30$

from above we concluded that $f$ is not continuous for any values of $a$ and $b$.