Find the Asymptotes f(x)=1/(x-3)

Problem

ƒ(x)=1/(x−3)

Solution

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

x−3=0

x=3

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

degree of numerator=0

degree of denominator=1

3. Apply the rule for horizontal asymptotes where the degree of the denominator is greater than the degree of the numerator.

(lim_x→∞)(1/(x−3))=0

y=0

4. Check for oblique asymptotes by determining if the degree of the numerator is exactly one higher than the degree of the denominator.

0<1

There are no oblique asymptotes.

Final Answer

Vertical: *x=3, Horizontal: *y=0

Want more problems? Check here!