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What is the equation of the horizontal asymptote of the function /(x)-3™ -77 A y=0 B. y=2 ⠀ C. y=3 D. y=-7 O O A B C D

What is the equation of the horizontal asymptote of the function /(x)-3™ -77 A y=0 B. y=2 ⠀ C. y=3 D. y=-7 O O A B C D

Algebra and Trigonometry (6th Edition)
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,...
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**Question:** What is the equation of the horizontal asymptote of the function \( f(x) = 3^{x^3} - 7 \)? **Options:** A. \( y = 0 \) B. \( y = 2 \) C. \( y = 3 \) D. \( y = -7 \) E. All of the Above <details> <summary>Explanation of Concepts:</summary> To determine the horizontal asymptote of the function \( f(x) = 3^{x^3} - 7 \), we consider the behavior of \( f(x) \) as \( x \) approaches positive or negative infinity. Since exponential functions grow rapidly, \( 3^{x^3} \) tends towards infinity as \( x \to \infty \) and tends towards zero as \( x \to -\infty \). Thus, horizontally, the function shifts down by 7, indicating that the horizontal asymptote is: \[ y = -7 \] Therefore, the correct option is D. </details>
Transcribed Image Text:**Question:** What is the equation of the horizontal asymptote of the function \( f(x) = 3^{x^3} - 7 \)? **Options:** A. \( y = 0 \) B. \( y = 2 \) C. \( y = 3 \) D. \( y = -7 \) E. All of the Above <details> <summary>Explanation of Concepts:</summary> To determine the horizontal asymptote of the function \( f(x) = 3^{x^3} - 7 \), we consider the behavior of \( f(x) \) as \( x \) approaches positive or negative infinity. Since exponential functions grow rapidly, \( 3^{x^3} \) tends towards infinity as \( x \to \infty \) and tends towards zero as \( x \to -\infty \). Thus, horizontally, the function shifts down by 7, indicating that the horizontal asymptote is: \[ y = -7 \] Therefore, the correct option is D. </details>
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