Find the Asymptotes f(x)=(x+5)/(x^2-5x-14)

Problem

ƒ(x)=(x+5)/(x2−5*x−14)

Solution

1. Factor the denominator to identify values where the function is undefined.

x2−5*x−14=(x−7)*(x+2)

2. Identify vertical asymptotes by finding the zeros of the denominator that do not cancel with the numerator.

(x−7)*(x+2)=0

⇒x=7,x=−2

3. Determine the horizontal asymptote by comparing the degrees of the numerator and the denominator.

degree of *(x+5)=1

degree of *(x2−5*x−14)=2

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

degree of numerator<degree of denominator⇒y=0

Final Answer

Vertical: *x=7,x=−2; Horizontal: *y=0

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