Here is a graph of a function, \(f(x)\).

For each of the following transformations, sketch the transformed graph and write its equation in terms of \(f\).

Translation by \(\begin{pmatrix}-2\\0\end{pmatrix}\)

Translation by \(\begin{pmatrix}0\\-4\end{pmatrix}\)

Stretch by factor \(3\) parallel to \(x\)

Stretch by factor \(\frac{1}{2}\) parallel to \(y\)