Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**End Behavior of Polynomial Functions**
**Objective:**
Choose the end behavior diagram that best describes the function.
Given the polynomial:
\[ P(x) = \frac{7}{8} x^7 - x^5 - 5x + 3 \]
**Instructions:**
Choose from the graphs on the right to find the correct end behavior of the function.
**Options:**
- **Graph A:**
- Left end arrow pointing downwards.
- Right end arrow pointing upwards.
- **Graph B:**
- Left end arrow pointing upwards.
- Right end arrow pointing upwards.
- **Graph C:**
- Both ends with arrows pointing downwards.
- **Graph D:**
- Left end arrow pointing upwards.
- Right end arrow pointing downwards.
**Analysis:**
Examine the degree and the leading coefficient of the polynomial to determine the correct end behavior. The function \( P(x) \) has a leading term \( \frac{7}{8} x^7 \), indicating an odd-degree polynomial with a positive leading coefficient. This suggests that as \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e5de73a-1cfc-4dfd-9ce4-0380553a7e5d%2Fc068dd3f-ea6e-405b-bcf6-e6e48d400f11%2F7s2phy_processed.png&w=3840&q=75)
Transcribed Image Text:**End Behavior of Polynomial Functions**
**Objective:**
Choose the end behavior diagram that best describes the function.
Given the polynomial:
\[ P(x) = \frac{7}{8} x^7 - x^5 - 5x + 3 \]
**Instructions:**
Choose from the graphs on the right to find the correct end behavior of the function.
**Options:**
- **Graph A:**
- Left end arrow pointing downwards.
- Right end arrow pointing upwards.
- **Graph B:**
- Left end arrow pointing upwards.
- Right end arrow pointing upwards.
- **Graph C:**
- Both ends with arrows pointing downwards.
- **Graph D:**
- Left end arrow pointing upwards.
- Right end arrow pointing downwards.
**Analysis:**
Examine the degree and the leading coefficient of the polynomial to determine the correct end behavior. The function \( P(x) \) has a leading term \( \frac{7}{8} x^7 \), indicating an odd-degree polynomial with a positive leading coefficient. This suggests that as \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \).
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