To solve the problem of identifying the correct transformation(s) that map Figure A to Figure A' based on the given graph:

1. Examine the Figures:

   • Figure A is on the left with coordinates at $(-5, 0)$ for its center.
   • Figure A' is on the right with coordinates at $(5, 0)$ for its center.

2. Determine the Transformation:

   • The figures appear to be mirror images across the y-axis, meaning there is a reflection over the y-axis.
   • This corresponds to option E (Horizontal or y-axis reflection), which is already checked.

3. Other Potential Transformations:

   • There is no evidence of rotation (like 90° or 180°) because the orientation of Figure A and A' is the same.
   • A translation could be possible, but the change in the x-coordinate specifically suggests a reflection rather than a simple horizontal translation.

Thus, option E (y-axis reflection) is correct, and it may be the only valid transformation. There is no need for additional transformations such as translation, rotation, or vertical reflection.

Would you like more details on why the other options are incorrect, or have any questions?

Here are some related questions to explore:

1. What is the difference between a translation and a reflection?
2. How does a 90° clockwise rotation affect a figure’s position?
3. Can multiple transformations lead to the same final figure?
4. What are the algebraic rules for reflecting a point over the y-axis?
5. How would you describe the effect of a 180° rotation on a figure?

Tip: When dealing with reflections, always check whether the axes or specific lines of symmetry are involved!