Consider the polynomial

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

Problem

Consider the polynomial p(x)=−4x5+7x3−2x+1p(x)=-4x^{5}+7x^{3}-2x+1. Answer the questions below without plotting exact points. (i) Determine whether the graph of p(x)p(x) is symmetric about the yy-axis, symmetric about the origin, or has no such symmetry. Give a brief reason. (ii) Evaluate lim⁡x→+∞p(x)\displaystyle\lim_{x\to+\infty}p(x) and lim⁡x→−∞p(x)\displaystyle\lim_{x\to-\infty}p(x). (iii) Using the information obtained in parts (i) and (ii), draw a rough sketch of the graph, clearly showing its end behaviour on both sides of the xx-axis.

Related theory

Browse the problem library