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The notion of an asymptote can be extended to include curves as well as lines. Specifically, we say that curves y = f(x) and y = g(x) are asymptotic as x → +∞ provided lim [f(x) − g(x)] = 0 x→+∞0 and are asymptotic as x→→→∞ provided lim [f(x) − g(x)] = 0 2118 -10,15) g(x) %9 = 9 (-8, -20) V 7 15 10 in 10 -10- -15- 2 = a) Determine a simpler function g(x) such that y Y asymptotic to y = g(x) as x → +∞ or x→→∞. HINT: Divide x -3 into x² - 3. I x² - 3 x - 3 b) Use the square points to graph y = g(x) on the grid. c) Determine the equation of the vertical asymptote. (6, -20) 8 10 12 is Vertical asymptote: x = d) Use the circular point to graph the vertical asymptote on the grid. 3

The notion of an asymptote can be extended to include curves as well as lines. Specifically, we say that curves y = f(x) and y = g(x) are asymptotic as x → +∞ provided lim [f(x) − g(x)] = 0 x→+∞0 and are asymptotic as x→→→∞ provided lim [f(x) − g(x)] = 0 2118 -10,15) g(x) %9 = 9 (-8, -20) V 7 15 10 in 10 -10- -15- 2 = a) Determine a simpler function g(x) such that y Y asymptotic to y = g(x) as x → +∞ or x→→∞. HINT: Divide x -3 into x² - 3. I x² - 3 x - 3 b) Use the square points to graph y = g(x) on the grid. c) Determine the equation of the vertical asymptote. (6, -20) 8 10 12 is Vertical asymptote: x = d) Use the circular point to graph the vertical asymptote on the grid. 3

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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The notion of an asymptote can be extended to include curves as well as lines. Specifically, we say that curves y = f(x) and y = g(x) are asymptotic as x → +∞ provided lim [f(x) = g(x)] = 0 20→+∞0 and are asymptotic as x→→∞ provided lim [f(x) — g(x)] = 0 ∞0-←x g(x): 10, 15) = -8 -6 - (-8, -20) L N 15 10 in 5 in -10- a) Determine a simpler function g(x) such that y = -15- asymptotic to y = g(x) as x → +∞ or x →→∞. HINT: Divide x 3 into x² - 3. Y x² 3 x - 3 - b) Use the square points to graph y = g(x) on the grid. c) Determine the equation of the vertical asymptote. 6 8 10 (6, -20) is 12 Vertical asymptote: x = d) Use the circular point to graph the vertical asymptote on the grid.
Transcribed Image Text:The notion of an asymptote can be extended to include curves as well as lines. Specifically, we say that curves y = f(x) and y = g(x) are asymptotic as x → +∞ provided lim [f(x) = g(x)] = 0 20→+∞0 and are asymptotic as x→→∞ provided lim [f(x) — g(x)] = 0 ∞0-←x g(x): 10, 15) = -8 -6 - (-8, -20) L N 15 10 in 5 in -10- a) Determine a simpler function g(x) such that y = -15- asymptotic to y = g(x) as x → +∞ or x →→∞. HINT: Divide x 3 into x² - 3. Y x² 3 x - 3 - b) Use the square points to graph y = g(x) on the grid. c) Determine the equation of the vertical asymptote. 6 8 10 (6, -20) is 12 Vertical asymptote: x = d) Use the circular point to graph the vertical asymptote on the grid.
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