Chapter 4: Q. 51 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$R (x) = \frac{6 x^{2} + 7 x - 5}{3 x + 5}$

Short Answer

Expert verified

$y = 2 x - 1$ is the oblique asymptote of given rational expression.

Step by step solution

Step 1. Given information

Given rational expression:

$R (x) = \frac{6 x^{2} + 7 x - 5}{3 x + 5}$

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,

$y = a x + b w i l l b e o b l i q u e a s y m p t o t e . y = 2 x - 1$

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.
$R (x) = \frac{6 x^{2} + 7 x - 5}{3 x + 5}$

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)=6x2+7x-53x+5

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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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$R (x) = \frac{6 x^{2} + 7 x - 5}{3 x + 5}$