Q10. State whether each sentence is t... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q10. (page 727)

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The rational function $y = \frac{2}{x 鈭� 1} + 3$ has a horizontal asymptote at $\underset{炉}{y = 3}$ .

Short Answer

Expert verified

The given statement is True.

Step by step solution

Step 1. State the concept of the horizontal asymptote.

For the function $y = f (x)$ if the value of either $\lim_{x 鈫� 鈭�} f (x) = L$ or $\lim_{x 鈫� 鈭� 鈭�} f (x) = L$ and L is a finite number, then $y = L$ is known as horizontal asymptote of the given function.

Step 2. Explanation of the statement.

Now, in the given equation $y = \frac{2}{x 鈭� 1} + 3$ to find the value of horizontal asymptote, take limits as:

$\begin{matrix} \lim_{x 鈫� 鈭�} f (x) = \lim_{x 鈫� 鈭�} (\frac{2}{x 鈭� 1} + 3) = \frac{2}{鈭� 鈭� 1} + 3 = 0 + 3 = 3 \\ \lim_{x 鈫� 鈭� 鈭�} f (x) = \lim_{x 鈫� 鈭�} (\frac{2}{x 鈭� 1} + 3) = \frac{2}{鈭� 鈭� 鈭� 1} + 3 = 0 + 3 = 3 \end{matrix}$

Step 3. Write whether the statement is true or false.

Since $\lim_{x 鈫� 鈭�} f (x) = 3$ and $\lim_{x 鈫� 鈭� 鈭�} f (x) = 3$ , so $y = 3$ is a horizontal asymptote of the given function. Therefore, the given statement 鈥淭he rational function $y = \frac{2}{x 鈭� 1} + 3$ has a horizontal asymptote at $\underset{炉}{y = 3}$ .鈥� is true.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The rational function $y = \frac{2}{x 鈭� 1} + 3$ has a horizontal asymptote at $\underset{炉}{y = 3}$ .

Short Answer

Step by step solution

Step 1. State the concept of the horizontal asymptote.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Logic and Functions

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.The rational functiony=2x鈭�1+3has a horizontal asymptote aty=3炉.

Short Answer

Step by step solution

Step 1. State the concept of the horizontal asymptote.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Logic and Functions

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The rational function $y = \frac{2}{x 鈭� 1} + 3$ has a horizontal asymptote at $\underset{炉}{y = 3}$ .