SOLUTION: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote. f(x)=(2x-3)/(x^2+2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote. f(x)=(2x-3)/(x^2+2)      Log On


   

Question 115517: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote.
f(x)=(2x-3)/(x^2+2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Horizontal Asymptote:

Since the degree of the numerator (which is 1) is less than the degree of the denominator (which is 2), the horizontal asymptote is always y=0

So the horizontal asymptote is y=0

Vertical Asymptote:

To find the vertical aysmptote(s), set the denominator equal to zero:

x%5E2%2B2=0 Set the denominator equal to zero


x%5E2=-2 Subtract 2 from both sides


x=sqrt%28-2%29 Take the square root of both sides

Since you cannot take the square root of a negative number, the answer is not a real number. So in this case, there are no vertical asymptotes