Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
-$f ( x ) = \frac { x ^ { 2 } + 4 x - 6 } { x - 2 }$
A)Horizontal asymptote: y = -2
B)Oblique asymptote: y = x + 6
C)Neither

Question

Quizplus · Accepted Answer

To determine the type of asymptote for the given rational function $f(x) = \frac{x^2 + 4x - 6}{x - 2}$, we compare the degrees of the numerator and the denominator. Since the degree of the numerator (which is 2) is one higher than the degree of the denominator (which is 1), the graph of the function will have an oblique (or slant) asymptote. To find the equation of the oblique asymptote, we divide the numerator by the denominator using polynomial long division or synthetic division. The quotient (ignoring the remainder) gives the equation of the oblique asymptote, which in this case is $y = x + 6$.

Determine Whether the Graph of the Rational Function Has a Horizontal