How do I find the horizontal asymptotes of these equations

Question

 f(x)=(8x-3)/root(16x^2+6)

and

f(x)=(2X^2-1)/root(6+x^4)  

 

 

 

Answer 1

(1)

The rational function 

To find horizontal asymptote, first find the degree of the numarator and  the degree of denominator.

Degree of the numarator =1 and the degree of denominator = 1.

Since the degree of the numerator is equal to the degree of the denominator,horizontal asymptote is the ratio of the leading coefficient of numarator and denominator.

Leading coefficient of numarator =   8, leading coefficient of denominator = √(16)

y  = 8/4

y = 2

y  = 2 is the horizontal asymptote.

Answer 2

(2)

The rational function 

To find horizontal asymptote, first find the degree of the numarator and  the degree of denominator.

Degree of the numarator =2 and the degree of denominator = 2.

Since the degree of the numerator is equal to the degree of the denominator, horizontal asymptote is the ratio of the leading coefficient of numarator and denominator.

Leading coefficient of numarator = 2, leading coefficient of denominator = √(1)

y  = 2/1

y = 2

y  = 2 is the horizontal asymptote.