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...
Related questions
Question
![**Task Description:**
Write an equation for the polynomial graphed below.
---
**Graph Analysis:**
The graph depicts a polynomial curve with the following characteristics:
1. **X-axis Intercepts:** The curve crosses the x-axis at approximately \( x = -3, x = 0.5, \) and \( x = 2.5 \).
2. **Y-intercept:** The curve crosses the y-axis at \( y = 0 \).
3. **Turning Points:**
- The curve has a turning point around \( x = -2 \), where it changes direction from increasing to decreasing.
- Another turning point is near \( x = 1.5 \), where the curve changes from decreasing to increasing.
4. **Behavior:**
- As \( x \) approaches \(- \infty\), \( f(x) \to -\infty \).
- As \( x \) approaches \(+ \infty\), \( f(x) \to +\infty \).
The overall shape suggests a polynomial function of at least the fourth degree, given the number of turning points.
---
**Equation Box:**
\[ f(x) = \]
Enter the polynomial equation that fits the described graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc12a34-ec96-45dd-af10-4cda8c86b1a3%2F12fda8ef-abd8-4a1d-88b9-89adefb4eb4b%2Ft7iqapr_processed.png&w=3840&q=75)
Transcribed Image Text:**Task Description:**
Write an equation for the polynomial graphed below.
---
**Graph Analysis:**
The graph depicts a polynomial curve with the following characteristics:
1. **X-axis Intercepts:** The curve crosses the x-axis at approximately \( x = -3, x = 0.5, \) and \( x = 2.5 \).
2. **Y-intercept:** The curve crosses the y-axis at \( y = 0 \).
3. **Turning Points:**
- The curve has a turning point around \( x = -2 \), where it changes direction from increasing to decreasing.
- Another turning point is near \( x = 1.5 \), where the curve changes from decreasing to increasing.
4. **Behavior:**
- As \( x \) approaches \(- \infty\), \( f(x) \to -\infty \).
- As \( x \) approaches \(+ \infty\), \( f(x) \to +\infty \).
The overall shape suggests a polynomial function of at least the fourth degree, given the number of turning points.
---
**Equation Box:**
\[ f(x) = \]
Enter the polynomial equation that fits the described graph.
Expert Solution
Step 1
Write the equation of the polynomial
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning