Chapter 4: Q. 52 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$R (x) = \frac{8 x^{2} + 26 x - 7}{4 x - 1}$

Short Answer

Expert verified

$y = 2 x + 7$ is the oblique asymptote for the given rational expression.

Step by step solution

Step 1. Given information

Given rational expression:

$R (x) = \frac{8 x^{2} + 26 x - 7}{4 x - 1}$

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, $n = 2, m = 1$

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

$y = a x + b w i l l b e o b l i q u e a s y m p t o t e y = 2 x + 7$

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.
$R (x) = \frac{8 x^{2} + 26 x - 7}{4 x - 1}$

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.R(x)=8x2+26x-74x-1

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

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$R (x) = \frac{8 x^{2} + 26 x - 7}{4 x - 1}$