Question

Is B. the right answer? if not then, which is?

Answer 1

We can rewrite the function as follows,

`\begin{gathered} r(x)=2(x-3)/(x-3)+(x+1)/(x-3) \\ r(x)=(2(x-3)+x+1)/(x-3) \\ r(x)=(2x-6+x+1)/(x-3) \\ r(x)=(3x-5)/(x-3) \end{gathered}`

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

`\begin{gathered} r(0)=(3(0)-5)/((0)-3) \\ r(0)=(5)/(3)=1.66666 \end{gathered}`

Therefore, by comparing these results with the given graphs, the answer is option B