Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer
possible.
-Oblique asymptote $y = x + 5$
A) $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { 5 x }$
B) $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { x }$
C) $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { 5 x }$
D) $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { x }$

Question

Quizplus · Accepted Answer

An oblique (or slant) asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator. The given oblique asymptote is $y = x + 5$, which means the division of the numerator by the denominator should result in a quotient of $x + 5$ plus a remainder. Option B, $f(x) = \frac{x^2 + 5x + 1}{x}$, directly matches this requirement because dividing $x^2 + 5x + 1$ by $x$ gives a quotient of $x + 5$ plus a remainder of $1/x$, which becomes negligible as $x$ approaches infinity, leaving the oblique asymptote $y = x + 5$.

Find a Rational Function That Satisfies the Given Conditions y=x+5y = x + 5y=x+5

Find a Rational Function That Satisfies the Given Conditions $y = x + 5$