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2. Find the equation of the horizontal asympto

2. Find the equation of the horizontal asympto

Calculus: Early Transcendentals
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...
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**Question 2:** Find the equation of the horizontal asymptote for the function \( f(x) = \frac{x - 100}{x - 100} \). **Options:** - \( \circ \) \( y = x \) - \( \circ \) \( y = 1 \) - \( \circ \) \( y = 0 \) - \( \circ \) There is no horizontal asymptote. **Explanation of Function:** The function given is \( f(x) = \frac{x - 100}{x - 100} \). This simplifies to 1 for all values of \( x \) except where the function is undefined (such as \( x = 100 \)). **Answer Analysis:** Since the function simplifies to 1, it suggests that the horizontal asymptote is \( y = 1 \), if existent. However, due to the nature of the simplification, horizontal asymptotes typically relate to behavior as \( x \) approaches infinity. In this case, \( f(x) \) remains constant at 1 (suggesting \( y = 1 \) as the continual behavior), thus indicating this is likely the answer. **Therefore, the correct choice is:** - \( \circ \) \( y = 1 \)
Transcribed Image Text:**Question 2:** Find the equation of the horizontal asymptote for the function \( f(x) = \frac{x - 100}{x - 100} \). **Options:** - \( \circ \) \( y = x \) - \( \circ \) \( y = 1 \) - \( \circ \) \( y = 0 \) - \( \circ \) There is no horizontal asymptote. **Explanation of Function:** The function given is \( f(x) = \frac{x - 100}{x - 100} \). This simplifies to 1 for all values of \( x \) except where the function is undefined (such as \( x = 100 \)). **Answer Analysis:** Since the function simplifies to 1, it suggests that the horizontal asymptote is \( y = 1 \), if existent. However, due to the nature of the simplification, horizontal asymptotes typically relate to behavior as \( x \) approaches infinity. In this case, \( f(x) \) remains constant at 1 (suggesting \( y = 1 \) as the continual behavior), thus indicating this is likely the answer. **Therefore, the correct choice is:** - \( \circ \) \( y = 1 \)
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