Chapter 4: Q. 6 (page 247)

Find the domain of each function. Find any horizontal, vertical, or oblique asymptotes.
$r (x) = \frac{x^{2} + 2 x - 3}{x + 1}$

Short Answer

Expert verified

The domain of the function is $\{x | x \neq 1\}$ , vertical asymptote is $x = - 1$ and oblique asymptote is at $y = x - 1$

Step by step solution

Step 1. Given Information

The given function is $r (x) = \frac{x^{2} + 2 x - 3}{x + 1}$

Step 2. Calculation

Substitute the denominator expression equal to 0 to find the domain.

$x + 1 = 0 x = - 1$

Thus, the domain of the function is $\{x | x \neq - 1\}$

Step 3. Calculation

The zeroes of denominator $x + 1$ is $- 1$

Thus, line $x = - 1$ is the vertical asymptote.

The rational function is improper since degree of numerator is greater than the degree of denominator.

We will be using the long division method to express the function as $P (x) = f (x) + \frac{r (x)}{q (x)}$

Thus, $P (x) = x - 1 + \frac{- 2}{x + 1}$

As $x \to \infty o r x \to - \infty$ ,

$\frac{- 2}{x + 1} \approx \frac{- 2}{x} \to 0$

Thus, $P (x) \to x - 1$ . The oblique asymptote is at $y = x - 1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the domain of each function. Find any horizontal, vertical, or oblique asymptotes.
$r (x) = \frac{x^{2} + 2 x - 3}{x + 1}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Probability and Statistics

Calculus

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the domain of each function. Find any horizontal, vertical, or oblique asymptotes.r(x)=x2+2x-3x+1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Probability and Statistics

Calculus

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the domain of each function. Find any horizontal, vertical, or oblique asymptotes.
$r (x) = \frac{x^{2} + 2 x - 3}{x + 1}$