Consider the function P(x) = (x + 9)²(x+5) The y-intercept is the point The x-intercept(s) is/are the point(s) As →∞, y → As →∞0, y → Question Help: Video
Consider the function P(x) = (x + 9)²(x+5) The y-intercept is the point The x-intercept(s) is/are the point(s) As →∞, y → As →∞0, y → Question Help: Video
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
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Question
![**Consider the function \(P(x) = (x + 9)^2(x + 5)\)**
---
**1. The y-intercept is the point:**
- \[ \boxed{} \]
---
**2. The x-intercept(s) is/are the point(s):**
- \[ \boxed{} \]
---
**3. As \( x \to \infty \), \( y \to \):**
- \[ \boxed{} \]
---
**4. As \( x \to -\infty \), \( y \to \):**
- \[ \boxed{} \]
---
**Question Help:**
- [](URL)
[Note: Ensure you click on the video link for a detailed explanation and example solutions related to this function.]
---
**Explanation of Concepts:**
- **Y-intercept**: The y-intercept is the value of \( y \) when \( x \) is 0.
- **X-intercepts**: Also known as roots, these are the values of \( x \) when \( P(x) = 0 \).
- **End Behavior**: This describes what happens to \( y \) as \( x \) approaches infinity (\( \infty \)) or negative infinity (-\( \infty \)).
---
**Use Cases:**
- **Identifying intercept points helps in graphing the function accurately.**
- **Understanding the end behavior is crucial for analyzing the long-term trends of the polynomial function.**
For additional support, please refer to educational videos and tutorials linked above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5178d97-debf-4e38-84bd-a0fb36219423%2F4d262822-a192-4e06-848a-4122cb3e3dee%2Fdp6j6cf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the function \(P(x) = (x + 9)^2(x + 5)\)**
---
**1. The y-intercept is the point:**
- \[ \boxed{} \]
---
**2. The x-intercept(s) is/are the point(s):**
- \[ \boxed{} \]
---
**3. As \( x \to \infty \), \( y \to \):**
- \[ \boxed{} \]
---
**4. As \( x \to -\infty \), \( y \to \):**
- \[ \boxed{} \]
---
**Question Help:**
- [](URL)
[Note: Ensure you click on the video link for a detailed explanation and example solutions related to this function.]
---
**Explanation of Concepts:**
- **Y-intercept**: The y-intercept is the value of \( y \) when \( x \) is 0.
- **X-intercepts**: Also known as roots, these are the values of \( x \) when \( P(x) = 0 \).
- **End Behavior**: This describes what happens to \( y \) as \( x \) approaches infinity (\( \infty \)) or negative infinity (-\( \infty \)).
---
**Use Cases:**
- **Identifying intercept points helps in graphing the function accurately.**
- **Understanding the end behavior is crucial for analyzing the long-term trends of the polynomial function.**
For additional support, please refer to educational videos and tutorials linked above.
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