Mathematics

Problem

Consider the polynomial

p(x)=-4x^{5}+7x^{3}-2x+1

. Answer the questions below without plotting exact points. a. (i) Determine whether the graph of

p(x)

is symmetric about the

y

-axis, symmetric about the origin, or has no such symmetry. Give a brief reason. b. (ii) Evaluate

\displaystyle\lim_{x\to+\infty}p(x)

and

\displaystyle\lim_{x\to-\infty}p(x)

. c. (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

x

-axis.

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