SOLUTION: Find the horizontal and vertical asymptotes of the following: A) f(x)= 2x+3/x+2 B) g(x)= 5x / x^2+1

Algebra ->  Rational-functions -> SOLUTION: Find the horizontal and vertical asymptotes of the following: A) f(x)= 2x+3/x+2 B) g(x)= 5x / x^2+1      Log On


   

Question 92310: Find the horizontal and vertical asymptotes of the following:
A) f(x)= 2x+3/x+2
B) g(x)= 5x / x^2+1
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
A) f(x)= (2x + 3)/(x + 2)
Vertical Asymptote:
x = -2 because of the denominator
Horizontal Asymptope:
y = 2 derived from graphing or:
lim[x ~> +inf] (2x + 3)/(x + 2)
lim[x ~> +inf] 2(x^0)/(x^0) H' Theory
2
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x+%2B+3%29%2F%28x+%2B+2%29%29
B) g(x)= 5x / (x^2 + 1)
Vertical Asymptote:
none because of the denominator
Horizontal Asymptope:
y = 0 derived from graphing or:
lim[x ~> +inf] 5x / (x^2 + 1)
lim[x ~> +inf] 5/(2x) H' Theory
(5/2) * lim[x ~> +inf] 1/x
(5/2)(0) = 0
But: g(0) = 0 ... no asymptote
graph%28800%2C200%2C-20%2C20%2C-2.5%2C2.5%2C5x+%2F+%28x%5E2+%2B+1%29%29