The graph of $y=f(x)$ is shown in the $xy$-plane. The function $f$ is defined by $f(x)=a{x}^3+b{x}^2+cx+d$, where $a,b,c,$ and $d$ are constants. The graph has a local maximum at $(x_1,2)$ and a local minimum at $(x_2,-1)$.

If $g(x)=f(x)-3$, for how many distinct real values of $x$ does $g(x)=0$?