Find the Asymptotes f(x)=(2x^2)/(x^2-4)

Problem

ƒ(x)=(2*x2)/(x2−4)

Solution

1. Identify vertical asymptotes by finding the values of x that make the denominator zero while the numerator is non-zero.

x2−4=0

(x−2)*(x+2)=0

x=2,x=−2

2. Identify horizontal asymptotes by comparing the degrees of the numerator and the denominator.

degree of *2*x2=2

degree of *x2−4=2

3. Calculate the limit as x approaches infinity to find the horizontal asymptote since the degrees are equal.

(lim_x→∞)((2*x2)/(x2−4))=2/1

y=2

4. Check for oblique asymptotes by noting that since a horizontal asymptote exists (the degree of the numerator is not exactly one greater than the degree of the denominator), there are no oblique asymptotes.

Final Answer

Vertical: *x=2,x=−2; Horizontal: *y=2

Want more problems? Check here!