Investigation

## Warm-up

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 $y$