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

\[ S(f(x))= -4 \, x + 4 \, f\left(5\right) \hspace{1em} \text{and} \hspace{1em} T(f(x))= 3 \, f\left(x\right) - 4 \, f'\left(-5\right) \]

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