Question

use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following function.

\\f(x) = \frac{x^2 - 9x + 20}{x^8 - 5x^7}\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the vertical asymptote(s) is/are \\(x = \\) \boxed{ }.
(use a comma to separate answers as needed.)

b. there are no vertical asymptotes.

Explanation:

Factor the numerator and denominator

$$ f(x) = \frac{x^2 - 9x + 20}{x^8 - 5x^7} = \frac{(x - 4)(x - 5)}{x^7(x - 5)} $$

Simplify the expression for \(x

eq 5\)

$$ f(x) = \frac{x - 4}{x^7}, \quad x eq 5 $$

Determine the vertical asymptotes

$$
LATEXBLOCK0
$$

Answer:

• A. The vertical asymptote(s) is/are x = 0 (Correct answer)
• B. There are no vertical asymptotes.