Consider the polynomial function .

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

Problem

Consider the polynomial function

p(x)=-3x^{6}+2x^{4}-7

. (i) Find the degree and the leading coefficient of

p(x)

. (ii) Describe the end behaviour of the graph of

p(x)

x\to\infty

and as

x\to-\infty

. (iii) State whether the graph of

p(x)

possesses any symmetry about the

y

‐axis or the origin. Give a brief justification for your answer.