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)

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) (Show Source): You can put this solution on YOUR website!
a)
Horizontal Asymptote:

Since the degree of the numerator (which is ) is less than the degree of the denominator (which is ), the horizontal asymptote is always

So the horizontal asymptote is

Vertical Asymptote:

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

Set the denominator equal to zero

Subtract 2 from both sides

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
RELATED QUESTIONS
Find the horizontal and vertical asymptotes of the following. Type �none� if the function (answered by stanbon,MathLover1)

Find the equations for the horizontal and vertical asymptotes of the following. Type... (answered by stanbon)

Find the equations for the horizontal and vertical asymptotes of the following. Type none (answered by stanbon)

Find the horizontal and vertical asymptotes of the following. Type �none� if the function (answered by jim_thompson5910)

Find the horizontal and vertical asymptotes of the following. Type �none� if the function (answered by stanbon)

Find the horizontal and vertical asymptotes of the following. Type none if the function... (answered by stanbon)

Find the equations of the horizontal and vertical asymptotes for the following. Type none (answered by solver91311)

5) Find the equations of the horizontal and vertical asymptotes for the following. Type (answered by jim_thompson5910)

5) Find the equations for the horizontal and vertical asymptotes of the following. Type... (answered by solver91311)