Find the Asymptotes f(x)=(2x)/(x-3)

Problem

ƒ(x)=(2*x)/(x−3)

Solution

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

x−3=0

x=3

2. Identify the horizontal asymptote by comparing the degrees of the numerator and the denominator.

degree of *2*x=1

degree of *x−3=1

3. Calculate the ratio of the leading coefficients since the degrees are equal.

y=2/1

y=2

4. Check for slant asymptotes by noting that the degree of the numerator is not exactly one higher than the degree of the denominator.

Slant Asymptote: None

Final Answer

Vertical Asymptote: *x=3, Horizontal Asymptote: *y=2

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