Consider the rational function A Find the domain B Find the

Consider the rational function:

A. Find the domain.

B. Find the vertical asymptotes.

C. Find the horizontal asymptotes.

D. Sketcht he graph of the function.

Solution

f(x)= x²/(x²+4)

A. domain

In a rational expression, the denominator must be non zero.ANd here there is no number which makes the denominator zero.

Therefore domain is (-infinity,infiinity)

B. Vertical asymptote

x^2 +4=0

x=+-2i

So there is no vertical asymptote

c. Horizontal asymptote

numerator\'s degree=denominator\'s degree

Therefore HA, y=numerator\'s leading coefficient/denominator\'s leading coefficient=1/1=1

D.