Find the Asymptotes f(x)=1/(x-5)

Problem

ƒ(x)=1/(x−5)

Solution

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

x−5=0

x=5

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.

y=0

4. Check for oblique asymptotes by noting that they only exist if the degree of the numerator is exactly one higher than the degree of the denominator.

Oblique Asymptote: None

Final Answer

Vertical: *x=5, Horizontal: *y=0

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