SOLUTION: Find the horizontal asymptote, if any, of the graph of the rational function. {{{g(x)=(6x^2)/(2x^2+1)}}} a){{{y=3}}} b){{{y=1/3}}} c){{{y=0}}} d){{{no_horizontal_asymptote}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the horizontal asymptote, if any, of the graph of the rational function. {{{g(x)=(6x^2)/(2x^2+1)}}} a){{{y=3}}} b){{{y=1/3}}} c){{{y=0}}} d){{{no_horizontal_asymptote}}      Log On


   

Question 155662: Find the horizontal asymptote, if any, of the graph of the rational function.
g%28x%29=%286x%5E2%29%2F%282x%5E2%2B1%29
a)y=3
b)y=1%2F3
c)y=0
d)no_horizontal_asymptote
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Find the horizontal asymptote, if any, of the graph of the rational function.
g%28x%29=%286x%5E2%29%2F%282x%5E2%2B1%29
a)y=3
b)y=1%2F3
c)y=0
d)no_horizontal_asymptote 

Rules for horizontal asymptotes:

1. If the largest exponent of x in the numerator is GREATER than the
largest exponent of x in the denominator, there is 
no_horizontal_asymptote.

2. If the largest exponent of x in the numerator is LESS than the
largest exponent of x in the denominator, the horizontal asymptote is the
x-axis, whose equation is 

y+=+0

3. If the largest exponent of x in the numerator is EQUAL to the
largest exponent of x in the denominator, the horizontal asymptote is 
horizontal line whose equation is

  

---------------------

In your function:

g%28x%29=%286x%5E2%29%2F%282x%5E2%2B1%29

the largest exponent of x in the numerator is 2, and 
the largest exponent of x in the denominator is also 2.
They are equal so we use rule 3:

the horizontal asymptote is 
horizontal line whose equation is

 

The coefficient of the largest exponent of x in the numerator is
6, and the coefficient of the largest exponent of x in the 
denominator is 2, so the horizontal asymptote is the line
whose equation is:

y=6%2F2
y=3

So the correct choice is (a)

Edwin