Find the slant asymptote of the function $f(x)=\frac{x^{2}+7}{x}$ .
A) $y=x^{7}$
B) $y=x^{3}$
C) $y=1$
D) $y=x^{2}$
E) $y=x$

Question

Quizplus · Accepted Answer

The slant asymptote of a rational function occurs when the degree of the numerator is exactly one more than the degree of the denominator. Here, the numerator $x^2 + 7$ has degree 2, and the denominator $x$ has degree 1. Performing polynomial long division of $x^2 + 7$ by $x$ gives a quotient of $x$, which is the equation of the slant asymptote.

Find the Slant Asymptote of the Function f(x)=x2+7xf(x)=\frac{x^{2}+7}{x}f(x)=xx2+7​ A) y=x7y=x^{7}y=x7 B) y=x3y=x^{3}y=x3

Find the Slant Asymptote of the Function $f(x)=\frac{x^{2}+7}{x}$
A) $y=x^{7}$ B) $y=x^{3}$