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.

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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.2: Transformations Of Quadratic Functions

Problem 25PPS

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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