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Example 1 Video Example 4 Use the guidelines to sketch the curve y = A. The domain is D. {x|x²-1=0) {x|x*11) 2x² lim x-00² 1 B. The x- and y-intercepts are both 0. C. Since f(-x) = f(x), the function fis even lim x-1 2x² lim x-1-x² lim = 2x² 2x² lim x--1-x²²-1 lim Therefore, the line y = X Since the denominator is 0 when x = ±1, we compute the following limits. 2x² <<=00 (-∞, -1),(-1,1),(1,00) 2x² = -00 = Therefore, the lines x = 1 and x= (using interval notation). . The curve is symmetric about the y-axis. is a horizontal asymptote. are vertical asymptotes. This information about limits and asymptotes enables us to draw the asymptotes in the following figure.

Example 1 Video Example 4 Use the guidelines to sketch the curve y = A. The domain is D. {x|x²-1=0) {x|x*11) 2x² lim x-00² 1 B. The x- and y-intercepts are both 0. C. Since f(-x) = f(x), the function fis even lim x-1 2x² lim x-1-x² lim = 2x² 2x² lim x--1-x²²-1 lim Therefore, the line y = X Since the denominator is 0 when x = ±1, we compute the following limits. 2x² <<=00 (-∞, -1),(-1,1),(1,00) 2x² = -00 = Therefore, the lines x = 1 and x= (using interval notation). . The curve is symmetric about the y-axis. is a horizontal asymptote. are vertical asymptotes. This information about limits and asymptotes enables us to draw the asymptotes in the following figure.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.1: Parabolas
Problem 67E
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Example 1 Video Example < Use the guidelines to sketch the curve y = A. The domain is C. {x|x²-10} = {x|x=+1} D. B. The x- and y-intercepts are both 0. lim_2x² = Since f(-x) = f(x), the function fis [even = lim 200²-1 x 100 100 1 lim x-1+x²2²-1 جمیرح (-∞, -1),(-1,1),(1,00) = 00 = -00 = 2 ₂2 Therefore, the line y = Since the denominator is 0 when x = ±1, we compute the following limits. 28-2 2x² lim x-1+x²- - 1 2x² lim x-1²-1 2x² 2x² ²-1 = 2x² lim x-1²-1 Therefore, the lines x = 1 and x = | (using interval notation). ✓✓ . The curve is symmetric about the y-axis. is a horizontal asymptote. are vertical asymptotes. This information about limits and asymptotes enables us to draw the asymptotes in the following figure.
Transcribed Image Text:Example 1 Video Example < Use the guidelines to sketch the curve y = A. The domain is C. {x|x²-10} = {x|x=+1} D. B. The x- and y-intercepts are both 0. lim_2x² = Since f(-x) = f(x), the function fis [even = lim 200²-1 x 100 100 1 lim x-1+x²2²-1 جمیرح (-∞, -1),(-1,1),(1,00) = 00 = -00 = 2 ₂2 Therefore, the line y = Since the denominator is 0 when x = ±1, we compute the following limits. 28-2 2x² lim x-1+x²- - 1 2x² lim x-1²-1 2x² 2x² ²-1 = 2x² lim x-1²-1 Therefore, the lines x = 1 and x = | (using interval notation). ✓✓ . The curve is symmetric about the y-axis. is a horizontal asymptote. are vertical asymptotes. This information about limits and asymptotes enables us to draw the asymptotes in the following figure.
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