A rational function is defined by g(x)= 7x^ 4 -2x^ 2 +9 -3x^ 4 +5x^ 3 +1 .

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

A rational function

g

is defined by

g(x)=\frac{7x^{4}-2x^{2}+9}{-3x^{4}+5x^{3}+1}.

(1) Part (a) — Limit as

x\to-\infty

(2) Part (b) — Limit as

x\to\infty

(3) Part (c) — Horizontal asymptote(s) (4) Part (d) — Comparison of end behavior