A polynomial has the following graph features: • –intercepts at and only

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

Problem

A polynomial

h

has the following graph features: •

x

–intercepts at

(-3,0), (-1,0)

and

(2,0)

only. •

y

–intercept at

(0,6)

. • For very large positive values of

x

, the values of

h(x)

become large negative numbers. Using only this information, answer the questions given below. (i) Determine the least possible degree of

h

and explain your reasoning. (ii) Write an explicit expression for

h(x)

with leading coefficient

-1

and integer coefficients that satisfies all the listed features. (iii) State, with justification, whether

h

is an even function, an odd function or neither.