Write a 3rd degree polynomial for the graph of the function shown below. You should expand your answer. You can use the f_x button to type an equation fairly easily. 5- -5 .5. 10 -5- -10-

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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**Transcription for Educational Website**

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**Problem Statement:**

"Write a 3rd degree polynomial for the graph of the function shown below. You should expand your answer. You can use the \( fx \) button to type an equation fairly easily."

**Graph Description:**

- **Axes:** The graph is plotted on a standard Cartesian coordinate system with the x-axis and y-axis clearly labeled.
- **X-Axis:** Ranges from -10 to 10.
- **Y-Axis:** Ranges from -10 to 10.
- **Curve Characteristics:**
  - The graph depicts a red curve representing a 3rd degree polynomial.
  - The curve starts below the x-axis on the left, then rises as it crosses the x-axis.
  - It dips back below the x-axis before rising sharply and extending upwards.
  - This curve suggests that there are likely two local extrema: one minimum and one maximum.
- **Behavior:**
  - The polynomial crosses the x-axis at three distinct points, indicating three real roots.
  - The graph demonstrates typical cubic behavior with an overall increase from left to right.

By analyzing the turning points and intercepts, the aim is to derive an equation representing this cubic polynomial behavior.
Transcribed Image Text:**Transcription for Educational Website** --- **Problem Statement:** "Write a 3rd degree polynomial for the graph of the function shown below. You should expand your answer. You can use the \( fx \) button to type an equation fairly easily." **Graph Description:** - **Axes:** The graph is plotted on a standard Cartesian coordinate system with the x-axis and y-axis clearly labeled. - **X-Axis:** Ranges from -10 to 10. - **Y-Axis:** Ranges from -10 to 10. - **Curve Characteristics:** - The graph depicts a red curve representing a 3rd degree polynomial. - The curve starts below the x-axis on the left, then rises as it crosses the x-axis. - It dips back below the x-axis before rising sharply and extending upwards. - This curve suggests that there are likely two local extrema: one minimum and one maximum. - **Behavior:** - The polynomial crosses the x-axis at three distinct points, indicating three real roots. - The graph demonstrates typical cubic behavior with an overall increase from left to right. By analyzing the turning points and intercepts, the aim is to derive an equation representing this cubic polynomial behavior.
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