The given function is:
[tex]f(x)=3^x+1[/tex]
It is required to choose which of the graphs represents the graph of the function.
To do this, find the y-intercept of the function by substituting x=0 and then compare it with the y-intercepts of the graphs.
Substitute x=0 into the equation of the function:
[tex]f(0)=3^0+1=1+1=2[/tex]
Hence, the y-intercept is 2.
The graph with the y-intercept 2 is the required graph.
The graph is:
