Graph the function, not by plotting points, but by starting from the graph of y = e in the figure below. y = ex-2 domain -4 range -4 -∞,∞ -2 State the asymptote. -2 y X y 4 2 -2 y 4 2 -2 y = 3x y = ex 2 y = 2x 2 4 4 State the domain and range. (Enter your answers using interval notation.) X X -4 -4 -2 -2 y 4 2 -2 y 2 -2 2 2 4 4 X X
Graph the function, not by plotting points, but by starting from the graph of y = e in the figure below. y = ex-2 domain -4 range -4 -∞,∞ -2 State the asymptote. -2 y X y 4 2 -2 y 4 2 -2 y = 3x y = ex 2 y = 2x 2 4 4 State the domain and range. (Enter your answers using interval notation.) X X -4 -4 -2 -2 y 4 2 -2 y 2 -2 2 2 4 4 X X
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
![### Graphing Exponential Functions
#### Objective
Graph the function \( y = e^x - 2 \), not by plotting points, but by using the graph of \( y = e^x \) as a reference.
#### Reference Graph
- The graph shown at the top of the image includes several exponential functions for comparison:
- \( y = e^x \)
- \( y = 2^x \)
- \( y = 3^x \)
These exponential functions all exhibit similar growth patterns, but with different rates of increase depending on the base of the exponent.
#### Given Function
The function to be graphed is:
\[ y = e^x - 2 \]
#### Steps to Graph \( y = e^x - 2 \):
1. **Understand the transformation:**
- The graph of \( y = e^x \) is shifted downward by 2 units because of the \(-2\) term.
2. **Identify key points and transformations:**
- Any point \((x, y)\) on the graph of \( y = e^x \) will correspond to \((x, y - 2)\) on the graph of \( y = e^x - 2 \).
#### Graph Options
Four graphs are provided, but only one of them correctly represents the function \( y = e^x - 2 \).
- The correct graph shows a downward shift of the original \( y = e^x \) graph. The correct graph is located at the bottom-left position of the four choices.
#### Domain and Range
- **Domain:** The domain of \( y = e^x - 2 \) is all real numbers (\(-\infty, \infty\)).
- **Range:** Since \( e^x \) is always positive and \( e^x \to \infty \) as \( x \to \infty \) and \( e^x \to 0 \) as \( x \to -\infty \):
- When \( e^x \) is shifted down by 2 units, the range of \( y = e^x - 2 \) becomes \((-2, \infty)\).
#### Asymptote
- **Horizontal Asymptote:** For \( y = e^x \), there is no asymptote, but for \( y = e^](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc840c2e-3c91-4264-9dad-5574b6dda8ed%2Ffa095acd-9d33-4dfe-970a-d5bc349e2fed%2Fmdntr58_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Exponential Functions
#### Objective
Graph the function \( y = e^x - 2 \), not by plotting points, but by using the graph of \( y = e^x \) as a reference.
#### Reference Graph
- The graph shown at the top of the image includes several exponential functions for comparison:
- \( y = e^x \)
- \( y = 2^x \)
- \( y = 3^x \)
These exponential functions all exhibit similar growth patterns, but with different rates of increase depending on the base of the exponent.
#### Given Function
The function to be graphed is:
\[ y = e^x - 2 \]
#### Steps to Graph \( y = e^x - 2 \):
1. **Understand the transformation:**
- The graph of \( y = e^x \) is shifted downward by 2 units because of the \(-2\) term.
2. **Identify key points and transformations:**
- Any point \((x, y)\) on the graph of \( y = e^x \) will correspond to \((x, y - 2)\) on the graph of \( y = e^x - 2 \).
#### Graph Options
Four graphs are provided, but only one of them correctly represents the function \( y = e^x - 2 \).
- The correct graph shows a downward shift of the original \( y = e^x \) graph. The correct graph is located at the bottom-left position of the four choices.
#### Domain and Range
- **Domain:** The domain of \( y = e^x - 2 \) is all real numbers (\(-\infty, \infty\)).
- **Range:** Since \( e^x \) is always positive and \( e^x \to \infty \) as \( x \to \infty \) and \( e^x \to 0 \) as \( x \to -\infty \):
- When \( e^x \) is shifted down by 2 units, the range of \( y = e^x - 2 \) becomes \((-2, \infty)\).
#### Asymptote
- **Horizontal Asymptote:** For \( y = e^x \), there is no asymptote, but for \( y = e^
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 14 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