a) Graph
$$
\begin{aligned}
&y_{1}=x^{3} \\
&y_{2}=x^{3}-3 x^{2}-3
\end{aligned}
$$
b) In both graphs, for values of $x>3$, do the functions increase or decrease as $x$ increases?
c) When the leading term of a polynomial function is $x^{3}$, the polynomial must increase as $x$ increases for $x>a$, where $a$ is some real number greater than 0 . Explain why this must be so.
d) In both graphs, for values of $x<-3$, do the functions increase or decrease as $x$ decreases?
e) When the leading term of a polynomial function is $x^{3}$, the polynomial must decrease as $x$ decreases for $x<a$, where $a$ is some real number less than 0 . Explain why this must be so.