Questions: Find the horizontal asymptote, if any, of the graph of the rational function. f(x) = 10x / (6x^2 + 1) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is . (Type an equation.) B. There is no horizontal asymptote.

Find the horizontal asymptote, if any, of the graph of the rational function. f(x) = 10x / (6x^2 + 1) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is . (Type an equation.) B. There is no horizontal asymptote.
Transcript text: Find the horizontal asymptote, if any, of the graph of the rational function. \[ f(x)=\frac{10 x}{6 x^{2}+1} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is $\square$ . (Type an equation.) B. There is no horizontal asymptote.
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Solution

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Solution Steps

Step 1: Finding Vertical Asymptotes

Solve $Q(x) = 0$. The solutions are the x-values of the vertical asymptotes, unless they also make $P(x) = 0$ in a way that simplifies the fraction. Vertical Asymptotes: -0.408_I, 0.408_I

Step 2: Finding Horizontal Asymptotes

Compare the degrees of $P(x)$ and $Q(x)$. Horizontal Asymptote: $y = 0$

Step 3: Finding Oblique Asymptotes

No Oblique Asymptote.

Final Answer:

Vertical Asymptotes: -0.408_I, 0.408_I Horizontal Asymptote: $y = 0 Oblique Asymptote: None

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