This is an Exponential Function which domain will be all the real x while the range will be all the y>0.
Basically the graph of your function will occupy only the first and second quadrant.
When x becomes very large positively your function also becomes large, it tends to INFINITY; for example, if you have x=100 then y=3^(100+1)=5xx10^47!!!!.
On the other hand when x becomes very large negatively your function becomes very small, it tends to ZERO; for example, if you have x=-100 then y=3^(-100+1)=6xx10^-48!!!!.
In plotting your function we can focus our attention around the origin choosing values of x not too big or small to allow us to actually "see", on the graph, the points we have.
Let us try with:
x=-3 then y=3^(-3+1)=3^(-2)=0.11;
x=-2 then y=3^(-2+1)=3^(-1)=0.33;
x=-1 then y=3^(-1+1)=3^0=1;
x=0 then y=3^(0+1)=3^1=3;
x=1 then y=3^(1+1)=3^(2)=9;
x=2 then y=3^(2+1)=3^(3)=27;
Plotting these points you get: