Asked by Anonymous
Sketch the graph of the function
f(x) = (x+4)3(x+1)(x−2)2(x−5)/
(x+3)2(x+1)(x−3)
f(x) = (x+4)3(x+1)(x−2)2(x−5)/
(x+3)2(x+1)(x−3)
Answers
Answered by
Steve
vertical asymptotes at -3,3
zeroes at -4,2,5
multiplicity 3,2,1
hole at x = -1 (x+1) occurs in both top and bottom
no horizontal asymptotes
http://www.wolframalpha.com/input/?i=((x%2B4)%5E3(x%2B1)(x%E2%88%922)%5E2(x%E2%88%925))%2F((x%2B3)%5E2(x%2B1)(x%E2%88%923))+for+-5%3C%3Dx%3C%3D6
zeroes at -4,2,5
multiplicity 3,2,1
hole at x = -1 (x+1) occurs in both top and bottom
no horizontal asymptotes
http://www.wolframalpha.com/input/?i=((x%2B4)%5E3(x%2B1)(x%E2%88%922)%5E2(x%E2%88%925))%2F((x%2B3)%5E2(x%2B1)(x%E2%88%923))+for+-5%3C%3Dx%3C%3D6
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