The function is defined for all real

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

The function

f(x)=\dfrac{4x}{x^{2}+1}

is defined for all real

x

. Describe the end behavior of

f

by stating its horizontal asymptote as

x\to\infty

and briefly explaining (in one sentence) how the degrees of the numerator and denominator dictate this result.