Quandaries
and Queries 

What are the equations of all horizontal and vertical asymptotes for the curve y=x/(x(x^{2}4))(the answer is y=0, x=2, x=2, but I want to know how to get that algebraically.And why isn't x=0 another asymptote?) 

Hi Abraham. To find the equations of the horizontal (or other type, like slant or parabolic) asymptote for a rational function, we examine the degrees of the polynomials in the numerator and denominator:
As for the vertical asymptotes, you set the denominator equal to zero and solve for the zeroes of the function. I believe in this case that x=0 is not an asymptote because the rational function can be reduced to y=1/(x^{2}4) and so there is no x factor left in the denominator. The factors from x^{2}4, namely x2 and x+2 are used to solve for the two vertical asymptotes by setting the factors to zero and solving: x=2 and x=2. Hope this helps, Leeanne 

