Show that the function given by $f(x) = 3x + 17$ is strictly increasing on $R$.

We have, $f(x) = 3x + 17$ …(i)
$f(x)$ being a polynomial function, is continuous and derivable on $R$.

Differentiating (i), w.r.t. $x$, we get $f(x) = 3 > 0\forall x \in R$
$\Rightarrow f$ is strictly increasing on $R$.