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Question

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                      x-> infty

2) If Function f is defined by:   f(x)= 2x^2-x+3 / x^2+5x-1

         find the value of K where Y=K is a horizontal asymptote.

3) The Vertical asymptotes of:   f(x)= x^2-9 / x^2-x-6  are X=K where...

4) The Curve: y= x+7 / (x+5)(x+3) has veritcal asymptote at

    x= -3.  Which of the following correctly describes the behaviorof the curve near x=-3 ?

a. As x-> -3^-, y->infty & As x-> -3^+, y->infty                   

b. As x-> -3^-, y-> -infty & As x-> -3^+, y->infty

c. As x-> -3^-, y->infty & As x-> -3^+, y-> -infty

d.  As x-> -3^-, y-> -infty & As x-> -3^+, y-> -infty                                 

Explanation / Answer

1. look at leading terms to get (4x^2)/(5x^2) = 4/5 = 0.80

2. same as above: (2x^2)/(x^2) = 2 so K = 2

3. need x^2 - x - 6 = 0 so (x-3)(x+2) = 0 so x = 3 or x = -2 and there are two answers: K = 3 or K = -2

4. for x < -3, x+7>0, x+5>0 and x+3<0, so +/(+ * -) = - and y tends to -infinity; for x > -3, x+7>0, x+5>0 and x+3>0, so +/(+ * +) = + and y tends to +infinity; ANSWER: b

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