Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

In graphing, what does the term "shift" mean?

1. A movement of the graph left or right without changing its shape

2. A change that distorts the graph's appearance

3. A modification of the graph's variables

4. A transformation that alters the area

The correct answer is: A movement of the graph left or right without changing its shape

The term "shift" in graphing specifically refers to the movement of the entire graph left or right along the x-axis, or up or down along the y-axis, without altering the shape or orientation of the graph. This movement affects the position of the graph but keeps its fundamental characteristics—like slope and curvature—intact. For example, if a graph of a function is shifted to the right by a certain number of units, every point on the graph moves that same distance right, resulting in a new graph that retains the original shape but is positioned differently. In contrast, changes that may distort the graph’s appearance—such as stretching or compressing—do not fall under the definition of a shift. Modifications of the graph's variables can involve altering the function itself, resulting in variations that change the graph beyond mere positional adjustments. Similarly, transformations that alter the area would involve scaling or manipulating dimensions rather than just shifting the graph. Therefore, the concept of a "shift" is distinct and clearly defined in terms of movement without shape alteration.