Question > ) Let r(x)-x) be the rational function graphed below. Let P(x) and g(

Question

Question > ) Let r(x)-x) be the rational function graphed below. Let P(x) and g(x) You may assume all interesting behavior happens at even integers. What are the zeros of p(x)? r- be al. ( What are the zeros of q(x)? r(x) Hole Evaluate the following. Write DNE if the limit does not exist 16-12-840 8 12 16 lim r(x)= lim r(x) = ld) On what interval(s) is r(x) continuous? lel. What are the vertical asymptotes of r(x)? Vhat is the end behavio x) Be specific What does the end behavior tell you about the relative degrees of p and q? Use the graph and your answers above to write a potential equation for r(x)

Explanation / Answer

4)

(a)

zero of p(x) is x=2

(b)

zeros of q(x) are x= -2,6

(c)

limx->6-r(x)=- ,limx->6+r(x)=

(d)

r(x) is continous on (-,-2)U(-2,6)U(6,12)U(12,)

(e)

vertical asymptotes of r(x) are x=-2, x=6

(f)

lim[x->-]r(x) =2 ,lim[x->]r(x) =2

r(x) has y=2 as horizontal asymptote.

(g)

yes. degree s of p and q are equal

(h)

potential function is r(x) =[2(x-2)3(x-12)]/[(x+2)2(x-6)(x-12)]or

r(x) =2(x4-18x3+84x2-152x+96)/(x4-14x3+4x2+216x+288)

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