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

Problem

ƒ(x)=2/(x−4)

Solution

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

x−4=0

x=4

2. Identify the horizontal asymptote 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 numerator is less than the degree of the denominator.

y=0

4. Check for oblique asymptotes by noting that since a horizontal asymptote exists, there are no oblique (slant) asymptotes.

Final Answer

Vertical: *x=4, Horizontal: *y=0

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