[tex]\begin{gathered} A)x=-3 \\ B)y=20 \\ c)There\:are\:no\:oblique\:asymptotes \end{gathered}[/tex]
1) Since we need to find the asymptote, algebraically, we need to proceed with the following process.
Horizontal Asymptotes
We need to resort to the following ratio:
[tex]\begin{gathered} R(x)=\frac{20x}{x+3} \\ \\ \:y=\frac{numerator's\:leading\:coefficient}{denominator's\:leading\:coefficient} \\ \\ y=\frac{20}{1} \\ \\ y=20 \end{gathered}[/tex]
Vertical Asymptotes
We need to find the mathematical undefined values. We know that the value of x can't be -3 otherwise, that would yield a numerator over zero. And that is not possible. So the vertical asymptote is x=-3
Oblique Asymptotes
There are no oblique asymptotes for this rational function.
2) So now, let's examine the options.
[tex]\begin{gathered} A)x=-3 \\ B)y=20 \\ C)There\:are\:no\:oblique\:asymptotes \end{gathered}[/tex]
