Find the Asymptotes f(x)=(2x^2)/(x^2-16)

Problem

ƒ(x)=(2*x2)/(x2−16)

Solution

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

x2−16=0

(x−4)*(x+4)=0

x=4,x=−4

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

degree of *2*x2=2

degree of *x2−16=2

3. Calculate the limit as x approaches infinity since the degrees are equal.

(lim_x→∞)((2*x2)/(x2−16))=2/1

y=2

4. Check for oblique asymptotes by noting that since the degree of the numerator is not exactly one higher than the degree of the denominator, none exist.

Final Answer

Vertical: *x=4,x=−4; Horizontal: *y=2

Want more problems? Check here!