To map Figure $J$ onto Figure $K$, we can analyze the transformations by comparing the orientation, position, and size of both figures. Here's a step-by-step approach to determine the series of transformations:

1. Reflection:

   • First, notice that Figure $J$ and Figure $K$ are mirror images of each other with respect to the x-axis. This suggests that a reflection over the x-axis is the first transformation.

2. Translation:

   • After reflecting, Figure $J$ would be below the x-axis, similar to the position of Figure $K$. Next, we observe that Figure $J$ must be translated to the right and downward to match the exact position of Figure $K$.
   • Specifically, the translation should move the figure 2 units to the right and 4 units down.

Transformation Sequence:

1. Reflect Figure $J$ over the x-axis.
2. Translate the reflected figure 2 units to the right and 4 units down.

These transformations will map Figure $J$ onto Figure $K$.

Would you like any further details on this solution? Here are some related questions you might find helpful:

1. What is the general formula for reflecting a point over the x-axis?
2. How can you determine the translation vector between two figures?
3. What are some common sequences of transformations used in geometry?
4. How does the orientation of a figure change after reflection?
5. How do you prove that a sequence of transformations is correct?

Tip: When working with transformations, always check the final position and orientation of the figure to ensure that the transformations were applied correctly.