Consider the following maps of polynomials \(S:\mathcal{P}\rightarrow\mathcal{P}\) and \(T:\mathcal{P}\rightarrow\mathcal{P}\) defined by

\[ S(h(x))= -x^{3} h\left(x\right) - 3 \, h\left(x\right) \hspace{1em} \text{and} \hspace{1em} T(h(x))= x^{3} - h\left(-4\right) \]

Explain why one these maps is a linear transformation and why the other map is not.