Find an equation for the graph sketched below 구 5- 4 -5 -4 -3 -2 |-1 2 3 4 5 -2 -3 -4 -5 -7 -8- 1. 3. 6

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...
icon
Related questions
Question
### Find an Equation for the Graph Sketched Below

**Graph Description:**
The graph provided is a plot on a Cartesian coordinate system with the x-axis ranging from -5 to 5 and the y-axis ranging from -8 to 8. The graph displays a curve characteristic of a horizontal asymptote. 

- The horizontal asymptote is observed at y = 4.
- The curve decreases sharply as x approaches -∞ and levels off as it approaches the horizontal asymptote.

**General Analysis:**
The behavior of the graph is typical of a type of exponential function where the function seems to approach a certain value (4 in this case) without reaching it, i.e., a horizontal asymptote at y = 4.

**Suggested Equation:**
Given the characteristics and shape, a possible equation of the graph might be:
\[ f(x) = 4 - e^{-x} \]

Here, \(e\) is the base of the natural logarithm. 

**Explanation:**
- \(4\): represents the horizontal asymptote as x approaches -∞, the function approaches 4.
- \( - e^{-x} \): gives the exponential decay approaching the asymptote as x increases.

### Application:
Type the equation \( f(x) = 4 - e^{-x} \) into the provided input box to verify if it correctly represents the sketched graph.
Transcribed Image Text:### Find an Equation for the Graph Sketched Below **Graph Description:** The graph provided is a plot on a Cartesian coordinate system with the x-axis ranging from -5 to 5 and the y-axis ranging from -8 to 8. The graph displays a curve characteristic of a horizontal asymptote. - The horizontal asymptote is observed at y = 4. - The curve decreases sharply as x approaches -∞ and levels off as it approaches the horizontal asymptote. **General Analysis:** The behavior of the graph is typical of a type of exponential function where the function seems to approach a certain value (4 in this case) without reaching it, i.e., a horizontal asymptote at y = 4. **Suggested Equation:** Given the characteristics and shape, a possible equation of the graph might be: \[ f(x) = 4 - e^{-x} \] Here, \(e\) is the base of the natural logarithm. **Explanation:** - \(4\): represents the horizontal asymptote as x approaches -∞, the function approaches 4. - \( - e^{-x} \): gives the exponential decay approaching the asymptote as x increases. ### Application: Type the equation \( f(x) = 4 - e^{-x} \) into the provided input box to verify if it correctly represents the sketched graph.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Parabolas
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning