#### Answer

$$y=3\sqrt{x+1},$$

#### Work Step by Step

Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=cf(x)$ by vertically stretching the graph of $y=f(x)$ by a factor of $c$.
Hence, to vertically stretch the graph of $y=\sqrt{x+1}$ by a factor of 3, we multiply the right hand side of this equation by $3$, and, thus, obtain the equation: $$y=3\sqrt{x+1}$$