Questions: Find the horizontal and vertical asymptotes of (f(x)). [ f(x)=frac5 xx+1 ] Find the horizontal asymptotes. Select the correct choice below and fill in any answer boxes within your choice. A. The horizontal asymptote(s) can be described by the line(s) (Type an equation. Use a comma to separate answers as needed.) B. There are no horizontal asymptotes.

$Find the horizontal and vertical asymptotes of (f(x)). [ f(x)=frac5 xx+1 ] Find the horizontal asymptotes. Select the correct choice below and fill in any answer boxes within your choice. A. The horizontal asymptote(s) can be described by the line(s) (Type an equation. Use a comma to separate answers as needed.) B. There are no horizontal asymptotes.$

Transcript text: Find the horizontal and vertical asymptotes of $f(x)$. \[ f(x)=\frac{5 x}{x+1} \] Find the horizontal asymptotes. Select the correct choice below and fill in any answer boxes within your choice. A. The horizontal asymptote(s) can be described by the line(s) $\square$ (Type an equation. Use a comma to separate answers as needed.) B. There are no horizontal asymptotes.

Solution

Solution Steps

Step 1: Finding Horizontal Asymptotes

Since $deg(P) = deg(Q)$, the horizontal asymptote is $y = 5$, where the leading coefficients of $P(x)$ and $Q(x)$ are 5 and 1 respectively.

Step 2: Finding Vertical Asymptotes

The vertical asymptotes occur at values of $x$ that make $Q(x) = 0$, provided these values do not also make $P(x) = 0$. Thus, the vertical asymptotes are at $x = [-1]$.

Step 3: Finding Oblique Asymptotes

Since $deg(P) \neq deg(Q) + 1$, there are no oblique asymptotes.