How do you find the vertical, horizontal or slant asymptotes for # (sqrt(x^4 + 6x^2 + 9)) / (2x^2 - 10)#?

1 Answer
Jul 12, 2018

Answer:

Vertical asymptote is at #x= +-sqrt5#
Horizontal asymptote: #y=0.5#, slant asymptote:absent

Explanation:

#f(x)=sqrt(x^4+6x^2+9)/(2x^2-10)# or

#f(x)=sqrt((x^2+3)^2)/(2( x^2-5)# or

#f(x)=((x^2+3))/(2( x^2-5)#

Vertical asymptote is at # x^2-5=0 or x^2=5 or x=+-sqrt5#

Horizontal asymptote: The degree of numerator and denominator

is same i.e #2# , so we have a horizontal asymptote at

#y =# (numerator's leading coefficient) / (denominator's leading

coefficient) #:. y= 1/2=0.5#

Slant asymptote: Since numerator's degree is not greater , we

have no slant asymptote.

Vertical asymptote is at #x= +-sqrt5#

Horizontal asymptote: #y=0.5#, slant asymptote:absent

graph{(sqrt(x^4+6x^2+9))/(2x^2-10) [-10, 10, -5, 5]} [Ans]