Find the Asymptotes f(x)=x/(x+4)

Problem

ƒ(x)=x/(x+4)

Solution

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

x+4=0

x=−4

2. Identify horizontal asymptotes by comparing the degrees of the numerator and the denominator. Since both the numerator x and the denominator x+4 are of degree 1, the horizontal asymptote is the ratio of the leading coefficients.

y=1/1

y=1

3. Check for slant asymptotes by comparing degrees. Since the degree of the numerator is not exactly one greater than the degree of the denominator, there is no slant asymptote.

Final Answer

Vertical Asymptote: *x=−4, Horizontal Asymptote: *y=1

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