2x2 + 22x + 72 f(x) = x2 + 11a – 102 First, find the critical values (there should be three): Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum. What is the local maximum for this graph: y = In addition to the vertical asymptotes, there is another asymptote. Give the equation for this asymptote: Hint: What is lim f(x)?
2x2 + 22x + 72 f(x) = x2 + 11a – 102 First, find the critical values (there should be three): Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum. What is the local maximum for this graph: y = In addition to the vertical asymptotes, there is another asymptote. Give the equation for this asymptote: Hint: What is lim f(x)?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Graph Analysis and Asymptotes – Educational Resource**
Given the function:
\[ f(x) = \frac{2x^2 + 22x + 72}{x^2 + 11x - 102} \]
**1. Finding Critical Values:**
**First, find the critical values (there should be three):**
\[ \text{(Input Box)} \]
**2. Identifying Local Maximum and Asymptotes:**
Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum.
**Local Maximum:**
\[ x = \, \text{(Input Box)} \]
\[ y = \, \text{(Input Box)} \]
**3. Additional Asymptotes:**
In addition to the vertical asymptotes, there is another asymptote.
Give the equation for this asymptote:
*Hint: What is* \(\lim_{x \to \pm \infty} f(x)\)?
\[ \text{(Input Box)} \]
**4. Range of the Function:**
Finally, give the range for the function \( f \).
\[ \text{range} = \, \text{(Input Box)} \]
---
This section is designed to guide students through the process of finding critical points, identifying asymptotes, and determining the range of a given rational function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bb7c04b-31f7-4ac4-b04e-9c07278fceb0%2F3db9cce3-5f57-4550-981e-9b2cad0f2952%2F27yqs4_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Graph Analysis and Asymptotes – Educational Resource**
Given the function:
\[ f(x) = \frac{2x^2 + 22x + 72}{x^2 + 11x - 102} \]
**1. Finding Critical Values:**
**First, find the critical values (there should be three):**
\[ \text{(Input Box)} \]
**2. Identifying Local Maximum and Asymptotes:**
Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum.
**Local Maximum:**
\[ x = \, \text{(Input Box)} \]
\[ y = \, \text{(Input Box)} \]
**3. Additional Asymptotes:**
In addition to the vertical asymptotes, there is another asymptote.
Give the equation for this asymptote:
*Hint: What is* \(\lim_{x \to \pm \infty} f(x)\)?
\[ \text{(Input Box)} \]
**4. Range of the Function:**
Finally, give the range for the function \( f \).
\[ \text{range} = \, \text{(Input Box)} \]
---
This section is designed to guide students through the process of finding critical points, identifying asymptotes, and determining the range of a given rational function.
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