hi. this is from my Curve Sketching (Rational Functions) lesson. can you please help with this question. i attached the format teacher used as well.

question=

r' - 1 f (x) f' ( x ) = 3-x2 2(x2 - 6)Curve Sketching - Rational Functions f (x) = _ 1+x-x x- 1 f'(x) =-1- (x - 1)2 2 f (x) = 7 (x - 1)3 A: Domain: RXER ( X+ B: Intercepts: y-int (0,-1) x-int (-0.62,0) and (1.62, 0) 41 X=0 : y= 1+0-02 = -1 =0 = H+X-x' =0 D -1 2-1 7 * = + 1+05 2 x = -0. 618, 1618 C: Asymptotes: Vertical Asymptote: X = 1 (if there are any vertical asymptotes, you need NO Horizontal Asymptote: Ata (num) 7 dealden) to check the behaviour on both sides of each) Slant Asymptote: deg(mun) -1 = deg(den) SA: Y = - x + (0.999 ) = - 1000. 999 - lim tlal = -00 D: Intervals of Increase/Decrease: * (1001) = 998. 949 kim f(x) 2 00 Critical Numbers: f" (x ) = 0 : -1 0 1 - R 12-12 =0 = DNE 1+2-12 - X + .. No critical #'s x-1 E: Local Extrema: Classify any local extrema and find their y-values here Site we do not have any critical #'s, there's no local extrema. Page 1 of 3F: Intervals of Concavity: Critical Numbers: " (*) =0 7 2 (2 - 1)3 =0 DNE . . No critical #'s G: Points of Inflection: Find the y-values for any points of inflection. Since we do not have any critical toumbers, we cannot find POls. H: Sketch 2