What happens if we apply more than one transformation to a graph?

Choose two of these transformations and apply them in turn starting with the function \(f(x)\). Sketch the resulting graph after you have applied one transformation and then the other. Does it matter which order you apply the two transformations?

Does the order matter for all pairs, some pairs or none of the pairs?

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 \(y\)

Would your answer be different if we had chosen a different set of transformations? Or a different starting function?