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Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function. x³-125 x-9x+20 H(x) = Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function has one vertical asymptote,. (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is. (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has no vertical asymptote. Find the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has one horizontal asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two horizontal asymptotes. The top asymptote is and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has no horizontal asymptote. Find the oblique asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function has one oblique asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two oblique asymptotes. The oblique asymptote with negative slope is and the oblique asymptote with positive slope is (Type equations. Use integers or fractions for any numbers in the equations.) O C. The function has no oblique asymptote.

Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function. x³-125 x-9x+20 H(x) = Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function has one vertical asymptote,. (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is. (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has no vertical asymptote. Find the horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has one horizontal asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two horizontal asymptotes. The top asymptote is and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has no horizontal asymptote. Find the oblique asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function has one oblique asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) OB. The function has two oblique asymptotes. The oblique asymptote with negative slope is and the oblique asymptote with positive slope is (Type equations. Use integers or fractions for any numbers in the equations.) O C. The function has no oblique asymptote.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Finding Asymptotes of a Rational Function** Consider the rational function \( H(x) = \frac{x^3 - 125}{x^2 - 9x + 20} \). We are tasked with finding the vertical, horizontal, and oblique asymptotes, if any, for the given function. ### Find the Vertical Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one vertical asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two vertical asymptotes. The leftmost asymptote is \(\_\_\_\_\_\) and the rightmost asymptote is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no vertical asymptote. ### Find the Horizontal Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one horizontal asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two horizontal asymptotes. The top asymptote is \(\_\_\_\_\_\) and the rightmost asymptote is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no horizontal asymptote. ### Find the Oblique Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one oblique asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two oblique asymptotes. The oblique asymptote with negative slope is \(\_\_\_\_\_\) and the oblique asymptote with positive slope is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no ob
Transcribed Image Text:**Finding Asymptotes of a Rational Function** Consider the rational function \( H(x) = \frac{x^3 - 125}{x^2 - 9x + 20} \). We are tasked with finding the vertical, horizontal, and oblique asymptotes, if any, for the given function. ### Find the Vertical Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one vertical asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two vertical asymptotes. The leftmost asymptote is \(\_\_\_\_\_\) and the rightmost asymptote is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no vertical asymptote. ### Find the Horizontal Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one horizontal asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two horizontal asymptotes. The top asymptote is \(\_\_\_\_\_\) and the rightmost asymptote is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no horizontal asymptote. ### Find the Oblique Asymptotes: Select the correct choice below and fill in the answer box(es) to complete your choice. - **A.** The function has one oblique asymptote, \(\_\_\_\_\_\). - (Type an equation. Use integers or fractions for any numbers in the equation.) - **B.** The function has two oblique asymptotes. The oblique asymptote with negative slope is \(\_\_\_\_\_\) and the oblique asymptote with positive slope is \(\_\_\_\_\_\). - (Type equations. Use integers or fractions for any numbers in the equations.) - **C.** The function has no ob
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