Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } - 4 x + 7 } { x + 2 }$$
A) $y = x - 6$
B) $x = y + 4$
C) $y = x + 11$
D) no oblique asymptote

Question

Quizplus · Accepted Answer

To find the equation of the oblique asymptote for the given function, we perform polynomial long division or use synthetic division for the numerator divided by the denominator. The quotient (ignoring the remainder) gives the equation of the oblique asymptote. For the given function $\frac{x^2 - 4x + 7}{x + 2}$, dividing $x^2 - 4x + 7$ by $x + 2$ gives a quotient of $x - 6$, which corresponds to the equation of the oblique asymptote $y = x - 6$.

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