Algebra-2

To find the horizontal asymptote for the function , we compare the degrees of the numerator and the denominator.

 

1.Identify the degrees:

The degree of the numerator 2x + 6 is 1.

The degree of the denominator x - 3 is also 1.

 

2.To find horizontal asymptotes compare the degree of the numerator "N” to the degree of the denominator “D”

Case 1 : if N < D, then horizontal asymptote is y = 0, the x-axis.

Case 2: if N = D, then the quotient obtained by the leading coefficients from N and D is the horizontal asymptote in a form of y = an/ad.

Case 3: if N > D, the quotient from long division (N polynomial divided by D polynomial) is the oblique asymptote in a form of y = the equation you got from long division.

 

Since N = D: We use Case 2, where the degrees are equal.

Find the horizontal asymptote: The horizontal asymptote is given by the quotient of the leading coefficients. The leading coefficient of the numerator is 2 and the leading coefficient of the denominator is 1. So,

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