Question

determine the horizontal or slant asymptote of the following function. enter any asymptote as an equation. if there is neither a horizontal asymptote nor slant asymptote, enter none.

\\f(x) = \frac{5x^5 - 4x + 6}{8x^5 - x + 9}\\

Explanation:

Compare degrees of numerator and denominator

$$
LATEXBLOCK0
$$

Calculate the limit as x approaches infinity

$$ \lim_{x \to \pm\infty} f(x) = \lim_{x \to \pm\infty} \frac{5x^5 - 4x + 6}{8x^5 - x + 9} = \lim_{x \to \pm\infty} \frac{5 - \frac{4}{x^4} + \frac{6}{x^5}}{8 - \frac{1}{x^4} + \frac{9}{x^5}} = \frac{5}{8} $$

State the horizontal asymptote equation

$$ y = \frac{5}{8} $$

Answer:

Determine the horizontal or slant asymptote of the following function. Enter any asymptote as an equation. If there is neither a horizontal asymptote nor slant asymptote, enter None.

\(f(x) = \frac{5x^5 - 4x + 6}{8x^5 - x + 9}\)

The horizontal asymptote is <blank>\(y = \frac{5}{8}\)</blank>.