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.
-$f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }$
A)Horizontal asymptote: y = 5
B)Oblique asymptote: y = 5x + 40
C)Neither

Question

Quizplus · Accepted Answer

The graph of the given rational function $f(x) = \frac{5x^2 + 20x + 30}{x - 4}$ has an oblique asymptote because the degree of the numerator is one more than the degree of the denominator. To find the equation of the oblique asymptote, perform polynomial long division or synthetic division. The quotient (ignoring the remainder) gives the equation of the oblique asymptote, which is $y = 5x + 40$.

Determine Whether the Graph of the Rational Function Has a Horizontal