Pls do parts E,F,G,H only. 2x2Use the guidelines to sketch the curve y =x2- 1A.The domain is{x | x2 - 1 + 0} = {x | x + ±1}|(-0, – 1) U (-1,1) U (1,00) (using interval notation).%DВ.The x- and y-intercepts are both 0.C.Since f(-x) = f(x), the function f isThe curve is symmetric about the y-axis.even2x22D.limX → +0 x2lim11x2Therefore, the line y2is a horizontal asymptote.Since the denominator is 0 when x =±1, we compute the following limits.2x2limX → 1+ x22x21limX → 1x212x2lim%Dx →-1+ x22x21limX → -1- X'1Therefore, the lines x = 1 and x = -1are vertical asymptotes. This information about limits andasymptotes enables us to draw the asymptotes in the following figure.y=2x=-1jI = x||8. 4x(x² – 1) – 2x² - 2x(x² – 1)2E. f'(x) =%3D%3DSince f'(x) > 0 when x < 0 (x * -1) and f'(x) < 0 when x > 0 (x + 1), f is increasing on the intervals (-o, -1) andand decreasing on the intervals (0, 1) andF. The only critical number is x = 0. Since f' changes from positive to negative atis a local maximum by the First Derivative Test.G. f"(x) = -4(x² – 1)² + 4x · 2(x² - 1)2x(x² – 1)ªSince the simplified numerator,> O for all x, we have the following.f"(x) > 0 + x2 - 1 > 0 +|x| >and f"(x) < 0 +|x| <Thus. the curve is concave upward on the intervals (-0, -1) and. It has no point of inflection since 1 andand concave downward onare not in the domain of f.H. Using the information in parts (E)-(G), we finish the sketch in the following figure.y= 2x=-1|

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2x2 Use the guidelines to sketch the curve y = x2 - 1 A. The domain is {x | x2 - 1 + 0} {x | x + +1} (-0, – 1) U (-1,1)U(1,00) (using interval notation). В. The x- and y-intercepts are both 0. C. Since f(-x) = f(x), the function f is even 8. The curve is symmetric about the y-axis. 2x2 D. lim lim 1 X- to 1 - x2 X - t00 x2 - 1 Therefore, the line y =| 2 is a horizontal asymptote. Since the denominator is 0 when x = ±1, we compute the following limits. 2x2 lim = 00 X→1+ x2 2x2 - 1 lim х> 1" х* —1 2x2 lim x → -1+ x² - 1 2x2 lim X → -1- x2 - 1 Therefore, the lines x = 1 and x = -1 are vertical asymptotes. This information about limits and fall.