Chapter 4: Q. 46 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$G (x) = \frac{x^{3} + 1}{x^{2} - 5 x - 14}$

Short Answer

Expert verified

$y = x + 5$ is the oblique asymptote for the given rational expression.

Step by step solution

Step 1. Given information

Given rational expression:

$G (x) = \frac{x^{3} + 1}{x^{2} - 5 x - 14}$

Step 2. Write the concept

If n = m + 1 (the degree of the numerator is one more than the degree of the denominator), the

quotient obtained is of the form ax + b (a polynomial of degree 1), and the line y = ax + b is an oblique

asymptote.

Step 3. Calculation

Here, $n = 3, m = 2$

Thus, $n = m + 1$ and therefore,

$y = a x + b w i l l b e t h e o b l i q u e a s y m p t o t e y = x + 5$

i.e. the quotient when we divide numerator with denominator.

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$G (x) = \frac{x^{3} + 1}{x^{2} - 5 x - 14}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.G(x)=x3+1x2-5x-14

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$G (x) = \frac{x^{3} + 1}{x^{2} - 5 x - 14}$