What is a transformation in mathematical terms?

A transformation in mathematical terms refers to an operation that changes the form or position of a shape or function. This can include various types of alterations, such as translations (shifting the position), rotations (turning around a point), reflections (flipping over a line), and dilations (resizing while maintaining shape). Each of these operations is essential in understanding how different shapes or functions relate to each other in geometry and algebra.

The choice that defines a transformation as an operation aligns with the fundamental concept of transformations in mathematics, which focuses on how figures can be manipulated while still retaining their essential characteristics, such as congruence or similarity. This understanding is crucial for analyzing geometric properties and behaviors of functions more broadly.

Other options presented do not precisely capture the comprehensive nature of transformations. For example, altering the size of a shape focuses only on dilations, while calculating area and solving equations pertain to different mathematical concepts that do not involve changes to shape or position. Therefore, the emphasis on both form and position in the correct answer accurately reflects the broader definition of transformations in mathematics.