SOLUTION: I need help when asked to find asymptotes of a rational function. For example: f(x)=x+2 ------ x sqrd-5x+6

Question 145523: I need help when asked to find asymptotes of a rational function. For example:
f(x)=x+2
------
x sqrd-5x+6
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given function

Looking at the numerator , we can see that the degree is since the highest exponent of the numerator is . For the denominator , we can see that the degree is since the highest exponent of the denominator is .

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 asymptote, just set the denominator equal to zero and solve for x

Set the denominator equal to zero

Now let's use the quadratic formula to solve for x. If you need help with the quadratic formula, check out this solver.

After using the quadratic formula, we get the solutions
or

So this means the vertical asymptotes are or

Notice if we graph , we can visually verify our answers:

Graph of with the horizontal asymptote (blue line) and the vertical asymptotes and (green lines)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x)=(x+2)/(xsqrt(5x+6))
---------
Vertical Asymptote when x = 0 and when 5x+6=0 or when x = -6/5.
Horizontal Asymptote: I graphed it to see one at y = 0
=====================
Cheers,
Stan H.

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