How do you determine horizontal,vertical and slant asymptotes for rational functions?

Question

biue · Answer

?

hayhayz · Answer

Hi Welcome to Openstudy!

irishboy123 · Answer

a function is a rational function if looks like this:

$$ f(x) = \frac{P(x)}{Q(x)} $$

a *ratio* of functions...

kinda obvious, maybe, but does that help?!

irishboy123 · Answer

so think:

Q = 0 
or
P = 0
or 
P = Q

candi5a18 · Answer

What if P=Q

comrad · Answer

Well an asymptote is where the graph of the equation does not touch

comrad · Answer

So if a graph doesn't touch the x axis, say the graph is a parabola. Your asymptote would be y=x

irishboy123 · Answer

you have $\dfrac{0}{0}$

and that's where you earn your money.....!!

but try to think of an example of that ......eg $\dfrac{sin (x) }{x}$...... and there is often a solution.

candi5a18 · Answer

I have a general idea on how to get horizontal and vertical asymtotes, I am confused about slant ones

candi5a18 · Answer

$$f(x)=\frac{x^2+2x+1}{x+2}$$
What is the slant asymptote for this function?

irishboy123 · Answer

|dw:1452723472130:dw|

like that?!