75 P(x) = xx'´ − x 5x+:

Algebra and Trigonometry (6th Edition)
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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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What is the end behavior?
**Arrows and Directions**

**Image Description:**

Four boxes are shown, each containing a different direction of curved arrows. The boxes are labeled A, B, C, and D.

- **Option A:** This box contains two arrows, each starting from the bottom corners and curving upward towards the top corners in a symmetrical fashion.
  
- **Option B:** In this box, one arrow starts at the bottom-right corner, curves up and to the left, and then points downward towards the bottom-left corner.
  
- **Option C:** This box features an arrow starting at the bottom-left corner and curving up and to the right, ending at the bottom-right corner.
  
- **Option D:** The arrow in this box begins at the bottom-left corner, curves upward, and continues to the top-right corner.

**Learning Objectives:**

- Recognize and interpret different arrow directions and their meanings.
- Understand how directionality can signify various relationships or movements in diagrams.
Transcribed Image Text:**Arrows and Directions** **Image Description:** Four boxes are shown, each containing a different direction of curved arrows. The boxes are labeled A, B, C, and D. - **Option A:** This box contains two arrows, each starting from the bottom corners and curving upward towards the top corners in a symmetrical fashion. - **Option B:** In this box, one arrow starts at the bottom-right corner, curves up and to the left, and then points downward towards the bottom-left corner. - **Option C:** This box features an arrow starting at the bottom-left corner and curving up and to the right, ending at the bottom-right corner. - **Option D:** The arrow in this box begins at the bottom-left corner, curves upward, and continues to the top-right corner. **Learning Objectives:** - Recognize and interpret different arrow directions and their meanings. - Understand how directionality can signify various relationships or movements in diagrams.
### Polynomial Function and Graph Selection

The polynomial function given is:

\[ P(x) = 2x^7 - x^5 - 5x + 4 \]

**Task:** Choose from the graphs on the right that best represents the polynomial function \( P(x) \).

**Explanation:**

- The leading term \( 2x^7 \) indicates that the function is a degree 7 polynomial, which is an odd degree, suggesting that the graph will have opposite end behaviors.
- Positive leading coefficient \( 2 \) means the graph rises to the right and falls to the left.
- Consider the influence of other terms, especially \( -x^5 \) and \( -5x \), which may affect the curvature and the intercept points of the graph.
- The constant \( +4 \) indicates the y-intercept of the polynomial function.

Examine the provided graphs to determine which one exhibits these characteristics. Ensure that the selected graph captures the degree, symmetry, and general shape expected from the given function.
Transcribed Image Text:### Polynomial Function and Graph Selection The polynomial function given is: \[ P(x) = 2x^7 - x^5 - 5x + 4 \] **Task:** Choose from the graphs on the right that best represents the polynomial function \( P(x) \). **Explanation:** - The leading term \( 2x^7 \) indicates that the function is a degree 7 polynomial, which is an odd degree, suggesting that the graph will have opposite end behaviors. - Positive leading coefficient \( 2 \) means the graph rises to the right and falls to the left. - Consider the influence of other terms, especially \( -x^5 \) and \( -5x \), which may affect the curvature and the intercept points of the graph. - The constant \( +4 \) indicates the y-intercept of the polynomial function. Examine the provided graphs to determine which one exhibits these characteristics. Ensure that the selected graph captures the degree, symmetry, and general shape expected from the given function.
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