Find the Asymptotes f(x)=1/(x-4)

Problem

ƒ(x)=1/(x−4)

Solution

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

2. Set the denominator equal to zero and solve for x

x−4=0

3. Solve for x to find the vertical asymptote.

x=4

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

5. Compare degrees where the degree of the numerator is 0 and the degree of the denominator is 1

6. Apply the rule that if the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is the x-axis.

y=0

Final Answer

Vertical Asymptote: *x=4, Horizontal Asymptote: *y=0

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