Find the verticle asymptote of the rational
function 
Possible answers:
y = 1/2
y = 3/4
y = 2
y = 4
Thank you. Exactly what is a asymptote? Can anyone
explain the simplest way to solve this problem?
-------------------------------------------------
Something is wrong! Asymptotes are straight
lines. All those choices are equations of
HORIZONTAL lines, not of VERTICAL lines.
Yet you asked for the VERTICAL asymptote. The
vertical asymptote has equation 
and the
HORIZONTAL asymptote has equation 
.
Did you copy something wrong? Did you type y's
where there should be x's, or did you type "verticle"
(sic) when you meant "horizontal"?
First I'll have to show you how to solve the
problem by graphing. Then I'll show you the simplest
way. But you must understand what an asymptote
is before you can know what you are doing.
Let's graph
Get some points:
x f(x)
-10 1
-7 1.1
-3 1.5
-2 1.8
0 6
2 -1
4 0
8 .4
11 .5
The graph of the function is in green. But
I have drawn two extra lines in, a blue vertical
line and a red horizontal line. These lines are
called "asymptotes". Look at the blue vertical
line that goes through 1/2 on the x-axis? The
green curve approaches that green line but never
touches it. That line is called the vertical
ASYMPTOTE. I also drew in the horizontal
asymptote in red.
As you can see, that green vertical asymptote has
the equation 
. and that blue
horizontal asymptote has the equation 
.
Now here is the easy way to find the equation of that blue
vertical asymptote without having to graph:
Set the denominator of equal
to zero, because a function is undefined if x has a value
which causes the function to be undefined. You know
that having a 0 in the denominator causes a fraction to be
undefined, right? So we have
That's all there is to finding the equation of the vertical
asymptote.
Now to find the horizontal asymptote, the red line.
Since numerator and denominator have the same degree
(same largest exponent of x), we merely get the
quotient of the coefficients of the largest powers
of x. The coefficient of x in the numerator is 3
and the coefficient of x in the denominator is
4, so we make the fraction
and write
as the equation of the red horizontal
asymptote.
Edwin
