We can rewrite the function as follows,
[tex]\begin{gathered} r(x)=2\frac{x-3}{x-3}+\frac{x+1}{x-3} \\ r(x)=\frac{2(x-3)+x+1}{x-3} \\ r(x)=\frac{2x-6+x+1}{x-3} \\ r(x)=\frac{3x-5}{x-3} \end{gathered}[/tex]
From this last result, we can see that the vertical asymptote ocurrs when x= 3. Then, the possible solutions are option b and option d.
On the other hand, the y-intercept ocurrs at x=0. Then, by replacing x=0 into the last result, we have
[tex]\begin{gathered} r(0)=\frac{3(0)-5}{(0)-3} \\ r(0)=\frac{5}{3}=1.66666 \end{gathered}[/tex]
Therefore, by comparing these results with the given graphs, the answer is option B
