Give the equation of the oblique asymptote, if any, of the function.
-$$h ( x ) = \frac { 3 x ^ { 2 } - 8 x - 4 } { 9 x ^ { 2 } - 4 x + 6 }$$
A) $y = x + \frac { 1 } { 3 }$
B) $y = \frac { 1 } { 3 }$
C) $y = \frac { 1 } { 3 } x$
D) no oblique asymptote

Question

Quizplus · Accepted Answer

The function $h(x) = \frac{3x^2 - 8x - 4}{9x^2 - 4x + 6}$ has the same degree in both the numerator and the denominator. When the degrees are the same, the oblique asymptote (if any) is found by dividing the leading coefficients. However, in this case, the function simplifies to a constant value as $x$ approaches infinity, indicating that there is no oblique asymptote. Instead, it approaches a horizontal asymptote, which is not listed among the options.

Give the Equation of the Oblique Asymptote, If Any, of the Function