Questions: Follow the steps for graphing a rational function to graph the function R(x)=8/(x^2-9). Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, 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 a negative slope is , and the oblique asymptote with a positive slope is . (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.

$Follow the steps for graphing a rational function to graph the function R(x)=8/(x^2-9). Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, . (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is , and the oblique asymptote with a positive slope is . (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.$

Transcript text: Follow the steps for graphing a rational function to graph the function $R(x)=\frac{8}{x^{2}-9}$. Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, $\square$ . (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymplotes. The oblique asymptote with a negative slope is $\square$ , and the oblique asymptote with a positive slope is $\square$ I. (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.

Solution

Solution Steps

Step 1: Identify the Rational Function

The given rational function is: \[ R(x) = \frac{8}{x^2 - 9} \]

Step 2: Determine the Oblique Asymptote

For a rational function $ \frac{p(x)}{q(x)} $, an oblique asymptote exists if the degree of $ p(x) $ is exactly one more than the degree of $ q(x) $. Here, the degree of the numerator $ 8 $ is 0, and the degree of the denominator $ x^2 - 9 $ is 2. Since the degree of the numerator is not greater than the degree of the denominator, there is no oblique asymptote.

Final Answer

C. There is no oblique asymptote.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = 8/(x^2 - 9)"], "latex_expressions": ["$y = \\frac{8}{x^2 - 9}$"]}

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