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Match f(x) with its graph without using a calculator. X-4 f(x) = O A. G O B. 10 Q G O C. 10 O D. Q P

Match f(x) with its graph without using a calculator. X-4 f(x) = O A. G O B. 10 Q G O C. 10 O D. Q P

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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explain how I do this without a calculator in detail

**Exercise: Matching a Function to its Graph** Objective: Match the function \( f(x) = \frac{x - 4}{x} \) with its corresponding graph without using a calculator. **Options:** - **Graph A:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 1 \). - The graph is in the form of two curves in the first and third quadrants, approaching but never touching the asymptotes. - **Graph B:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal line at \( y = -1 \). - The graph has two curves in the second and fourth quadrants. - **Graph C:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal line at \( y = 1 \). - The graph has two curves, similar to Graph A, but mirrored across the y-axis. - **Graph D:** - A hyperbola with a vertical asymptote at \( x = 0 \) and horizontal line at \( y = 4 \). - The graph is similar to Graph B but approaches a different horizontal line. **Note:** Each graph is labeled with its corresponding option. Consider the behavior of the function \( f(x) = \frac{x - 4}{x} \) for vertical and horizontal asymptotes when determining the correct match.
Transcribed Image Text:**Exercise: Matching a Function to its Graph** Objective: Match the function \( f(x) = \frac{x - 4}{x} \) with its corresponding graph without using a calculator. **Options:** - **Graph A:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 1 \). - The graph is in the form of two curves in the first and third quadrants, approaching but never touching the asymptotes. - **Graph B:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal line at \( y = -1 \). - The graph has two curves in the second and fourth quadrants. - **Graph C:** - A hyperbola with a vertical asymptote at \( x = 0 \) and a horizontal line at \( y = 1 \). - The graph has two curves, similar to Graph A, but mirrored across the y-axis. - **Graph D:** - A hyperbola with a vertical asymptote at \( x = 0 \) and horizontal line at \( y = 4 \). - The graph is similar to Graph B but approaches a different horizontal line. **Note:** Each graph is labeled with its corresponding option. Consider the behavior of the function \( f(x) = \frac{x - 4}{x} \) for vertical and horizontal asymptotes when determining the correct match.
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