Given the following functions find the following: a. Domain b. The Vertical Asymptote(s) c. The Horizontal Asymptote f(x) = (4x)/(2x^(2) +1)

Question

Given the following functions find the following:

a. Domain
b. The Vertical Asymptote(s)
c. The Horizontal Asymptote


`f(x) = (4x)/(2x^(2) +1)`

Answer 1

The asymptotes are found using the rational function ax^n/ bx^m where n is the degree of the numerator and m is the degree of the denominator.

In the given equation the numerator isn’t raised to any power so n is considered equal to 1. The Demi actor has x raised to the 2nd power so m equals 2.

If n < m then the c axis, y= 0 is the horizontal asymptote.

Also because n is less than m there are no vertical asymptote.

The domain is any real number so the domain would be (-infinity, infinity)