Find the Asymptotes f(x)=(x^2+4x-7)/(x-8)

Problem

ƒ(x)=(x^2+4*x−7)/(x−8)

Solution

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

x−8=0

x=8

2. Check for horizontal asymptotes by comparing the degrees of the numerator and denominator. Since the degree of the numerator (2 is exactly one greater than the degree of the denominator (1, there is no horizontal asymptote.

3. Identify the slant asymptote by performing polynomial long division or synthetic division on the expression.

(x^2+4*x−7)/(x−8)=x+12+89/(x−8)

4. Determine the slant asymptote equation from the linear part of the quotient obtained in the previous step.

y=x+12

Final Answer

Vertical Asymptote: *x=8, Slant Asymptote: *y=x+12

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