Define the piecewise rational function h(x)= cases 4x^ 5 -x^ 2 +6 2x^ 5 +9 , & x 0,…

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

Problem

Define the piecewise rational function

h(x)=\begin{cases} \dfrac{4x^{5}-x^{2}+6}{2x^{5}+9}, & x\ge 0,\\ \dfrac{-5x^{5}+3x}{x^{5}-2x^{2}+1}, & x<0. \end{cases}

(1) Part (a) — Limit as

x\to\infty

(2) Part (b) — Limit as

x\to-\infty

(3) Part (c) — Discussion of horizontal asymptote(s)