Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What does translation in graphing involve?

1. A form of stretching or compressing the graph

2. A shift of a graph that changes its shape

3. A shift of a graph horizontally, vertically, or both

4. A rotation of the graph around an axis

The correct answer is: A shift of a graph horizontally, vertically, or both

Translation in graphing specifically refers to the movement of a graph in a particular direction without altering its shape or size. This means that all points on the graph are moved the same distance in the same direction. By translating a graph horizontally, vertically, or both, the overall structure of the graph remains unchanged; only its position on the coordinate plane is affected. This process can be understood with respect to equations of functions, where adding or subtracting values inside the function alters the horizontal position, and modifying outside the function affects the vertical position. Therefore, the correct understanding of translation reflects this property of shifting the graph rather than changing its shape, which distinguishes it from other transformations like stretching, compressing, or rotating.