#### Answer

The sum of two continuous functions is continuous.

#### Work Step by Step

We are given the function $ f(x)=3x+4\sin x $. By Theorem 2 and 3, $3x $ and $4\sin x $ are continuous functions. Using the basic laws of continuity, the sum of two continuous functions is continuous; that is
$$ f(x)=3x+4\sin x $$
is continuous.