Answer to Question #91575 in Geometry for Sajid

Question

Q. Choose the correct answer.
Q.Which of the following are asymptotes of the curve represented by y2=(x-4)/x2(x+4) ?
a. x=-4
b. x=0
c. x=4
d. y=0

Answer 1

we decompose this function into two:

y₁=√((x-4)/(x^2*(x+4)));

y₂=-√((x-4)/(x^2*(x+4)));

find the limits of these functions for x->∞ and x->-∞.

and conclude the equation of a horizontal asymptote is y=0.

find the discontinuity points of the functions ( using the denominator ): x=-4 and x=0 (they will be the same for both functions);

Functions aborted on x∈[-4;4) which means that the point x=0 cannot be an asymptote;

finding the limits of lim(x->-4+0) and lim(x->-4-0) for each of two functions we obtain that x=-4 is a vertical asymptote.

Anwser: a, d