Question

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Sketch the graph of the function. Identify 1. Vertical and horizontal asymptotes 2. X and Y intercepts 3. The interval that your function increasing or decreasing f(x)= X-2 x+1

Answer 1

f2) = 2-22 x-2 2+1 1. vertical asymptotes : Let x=L is a vertical asymptote of the function. y = had it the limit of the function at this point is infinite. at means that : the points where denominator equals or does not exist. 0 2+1) =0 2= -1 OY How lim xtadt Then x=-1 is a vertical asymptote. Horizontal asymptotes lim Xod Cont) x-2 2+1 lim xoo delte It 1 and limo (1272 - 1 Thus: y = 1 is a horizontal asymptote. 2. For re-intercepts ! f02- O 2-2 +1 o Or, 2 = 2 Thus. (2,0) be the x-intercepts for-y-intercepts 2=0 f(x)=-2 so (0-2) be the ya intercepts.

در) row f' cao (441) 2 (72) (2+1) & (2-2)=(x-2). (x+1) (attaa+2) 3 (x+1)2 (241)2 sign diagram for f'(a). 2 We drow ttttty tttttt to -1 function be increasing on: cas-d) U (-1,0) The function be decreasing on: The Graph : y=1 (2,0) 2--1 2 100,-2)