Give the equation of the slant asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } - 6 x + 3 } { x + 7 }$$
A)y = x + 9
B)none
C)y = x - 13
D)x = y + 6

Question

Quizplus · Accepted Answer

To find the slant (oblique) asymptote of the function $f(x) = \frac{x^2 - 6x + 3}{x + 7}$, we perform polynomial long division or synthetic division. The quotient (ignoring the remainder) gives the equation of the slant asymptote. Dividing $x^2 - 6x + 3$ by $x + 7$, we get a quotient of $x - 13$, which means the slant asymptote is $y = x - 13$.

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