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

Cubic shaped graph crossing the x-axis at -1 and touching it at 2, and crossing the y-axis at 4

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 \(y\)

To get an idea of what a transformed graph looks like, identify a few key points on the graph and apply the transformations to those points. What would be the key points on our \(f(x)\) graph? You might find that some points are not so informative with certain transformations.