Algebra and Trigonometry (6th Edition)
6th Edition
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,...
Related questions
Question
![**Long Run Behavior of Exponential Functions**
In this exercise, we examine the function \( f(x) = -2(4)^x - 3 \) to understand its behavior as \( x \) approaches positive and negative infinity.
1. **Behavior as \( x \to -\infty \):**
For \( x \to -\infty \), evaluate the expression:
\[
\lim_{{x \to -\infty}} f(x) = ?
\]
Here, \( (4)^x \) approaches 0, making the function tend towards:
\[
\lim_{{x \to -\infty}} f(x) = -3
\]
2. **Behavior as \( x \to \infty \):**
For \( x \to \infty \), evaluate the expression:
\[
\lim_{{x \to \infty}} f(x) = ?
\]
Here, \( (4)^x \) grows exponentially large making the function tend towards:
\[
\lim_{{x \to \infty}} f(x) = -\infty
\]
### Summary:
- As \( x \to -\infty \), \( f(x) \to -3 \)
- As \( x \to \infty \), \( f(x) \to -\infty \)
Feel free to move on to the next question to further build on this concept.
](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ed96b38-bb6c-4f0b-a794-43dac03e0984%2F94c60506-6979-48d5-b041-dc7639d8b97a%2Fr1lvo1p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Long Run Behavior of Exponential Functions**
In this exercise, we examine the function \( f(x) = -2(4)^x - 3 \) to understand its behavior as \( x \) approaches positive and negative infinity.
1. **Behavior as \( x \to -\infty \):**
For \( x \to -\infty \), evaluate the expression:
\[
\lim_{{x \to -\infty}} f(x) = ?
\]
Here, \( (4)^x \) approaches 0, making the function tend towards:
\[
\lim_{{x \to -\infty}} f(x) = -3
\]
2. **Behavior as \( x \to \infty \):**
For \( x \to \infty \), evaluate the expression:
\[
\lim_{{x \to \infty}} f(x) = ?
\]
Here, \( (4)^x \) grows exponentially large making the function tend towards:
\[
\lim_{{x \to \infty}} f(x) = -\infty
\]
### Summary:
- As \( x \to -\infty \), \( f(x) \to -3 \)
- As \( x \to \infty \), \( f(x) \to -\infty \)
Feel free to move on to the next question to further build on this concept.
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 4 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education