How do you find the horizontal asymptote for #(x^2 - 5x + 6)/ (x - 3)#?

Question

Theodore Amidon · Accepted Answer

There isn't one.

The rules for horizontal asymptotes: When the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. When the degree of the numerator is the same as the degree of the denominator, there is a horizontal asymptote at #x=0#. When the degree of the numerator is less that the degree of the denominator, there is a horizontal asymptote at the quotient of the leading coefficients. Because, in this function, the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Madelyn Anderson · Answer

undefined To find the horizontal asymptote of the function $ \frac{x^2 - 5x + 6}{x - 3} $, examine the behavior of the function as $ x $ approaches positive or negative infinity.

Since the degree of the numerator is equal to the degree of the denominator, divide the leading coefficient of the numerator by the leading coefficient of the denominator to determine the horizontal asymptote.

In this case, the leading coefficients are both 1, so the horizontal asymptote is at $ y = 1 $.