Chapter 4: Q. 8 (page 234)

In Problems $7 - 44$ , follow Steps $1$ through $7$ on page $228$ to analyze the graph of each function.
$R (x) = \frac{x}{(x - 1) (x + 2)}$

Short Answer

Expert verified

The graph for the function $R (x) = \frac{x}{(x - 1) (x + 2)}$ is,

Step by step solution

Step 1 Given function is,

$R (x) = \frac{x}{(x - 1) (x + 2)}$

The domain of $R$ is, $\{x | x \neq 1, x \neq - 2\}$ .

Also, $R$ is in the lowest terms.

The $x$ - intercept can be found by determining the real zeros of the numerator of $R$ which is written in the lowest terms at $x = 0$ .

Here, the value of $R$ is $0$ when $x = 0$ . Hence, the $y$ - intercept is, $0$ .

Step 2 We can find the vertical asymptotes by finding the real zeros of the denominator of the function R.

The vertical asymptotes are, $x = \{1, - 2\}$ .

There is no horizontal asymptote of the graph. So, let us find the oblique asymptote.

This can be found by dividing the numerator by the denominator and the part except the remainder is the asymptote.

$y = \frac{x}{(x - 1) (x + 2)}$

Hence, the given polynomial has neither oblique nor horizontal asymptote.

Step 3 Now plot a graph by using the known values.

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.

In Problems $7 - 44$ , follow Steps $1$ through $7$ on page $228$ to analyze the graph of each function.
$R (x) = \frac{x}{(x - 1) (x + 2)}$

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 We can find the vertical asymptotes by finding the real zeros of the denominator of the function R.

Step 3 Now plot a graph by using the known values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Calculus

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 7-44, follow Steps 1through 7on page 228to analyze the graph of each function.Rx=xx-1x+2

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 We can find the vertical asymptotes by finding the real zeros of the denominator of the function R.

Step 3 Now plot a graph by using the known values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Calculus

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems $7 - 44$ , follow Steps $1$ through $7$ on page $228$ to analyze the graph of each function.
$R (x) = \frac{x}{(x - 1) (x + 2)}$