Each drop down box is the same ### Understanding Exponential Functions: Long Run BehaviorIn this section, we will analyze the long-run behavior of the function:\[ f(x) = -2 \cdot (4)^x - 3 \]To understand the behavior of \( f(x) \) as \( x \) approaches positive and negative infinity, consider the questions and explanations provided below.#### Exploration of \( f(x) \) as \( x \) Approaches Negative Infinity**Question:**As \( x \rightarrow -\infty \), \( f(x) \rightarrow \) ?Options for selection:- ?- \(\infty\)- \(-\infty\)- 0- -3**Explanation:**Trace the behavior of the function as \( x \) moves toward negative infinity.#### Exploration of \( f(x) \) as \( x \) Approaches Positive Infinity**Question:**As \( x \rightarrow \infty \), \( f(x) \rightarrow \) ?Options for selection:- ?- \(\infty\)- \(-\infty\)- 0- -3**Explanation:**Assess the behavior of the function when \( x \) progresses toward positive infinity.Click the "Next Question" button to continue with the practice and consolidate your learning.---**Diagram/Graph Explanation:**Currently, there is no visual graph provided, but envision the graph of the given exponential function \( f(x) \). 1. **As \( x \) approaches \(-\infty\)**: - \( 4^x \) becomes a very small positive number approaching 0 because any positive number raised to a large negative power tends to zero. - Therefore, \( f(x) \approx -3 \).2. **As \( x \) approaches \(\infty\)**: - \( 4^x \) grows exponentially. Since it's multiplied by \(-2\), the term \(-2 \cdot 4^x\) will become very large but negative. - Thus, \( f(x) \rightarrow -\infty \).Understanding these behaviors will help you in analyzing the general trends of exponential functions.

Explaination of the answer is as follows

Answered: Describe the long run behavior of f(x)…

Describe the long run behavior of f(x) = -2(4)²-3 As →-00, f(x) → ? ✓ As x→∞o, f(x) → ? ✓ ? > Next Question 8 -00 0 -3

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,...

Similar questions

assist with A,B,C,D
Simplify. i174
Blake answered 2/3 of the questions on his quiz correctly. If he answered 22 questionscorrectly, how many questions were on the quiz?
do question 9
You are the manager of World Wide Athlete, a chian of six sporting goods stores
Find leg
of Haw. csch? %3D Howe
Kara is sorting buttons by length for a craft project.the line plot shows the length of each button l.if Kara lines up all the 3/4-inch buttons,what would be the the total length
Raiza. Florence and Jeene are teenagers. The product of their ages, in years, is 4590. None of them are the same age. What are their ages?