What does a line graph representing data in a single-case design primarily aim to do?

A line graph representing data in a single-case design is primarily intended to track and evaluate client-specific goals visually. This visual representation allows practitioners to observe trends over time, facilitating a clear understanding of how a client's performance changes in relation to specific interventions or goals. By plotting individual data points across time, the graph provides insight into the effectiveness of the interventions being applied and helps identify patterns or fluctuations that might require adjustments in practice.

The focus on client-specific goals is crucial in single-case designs, as practitioners are often interested in the individual progress of a client rather than broader averages. This approach helps in tailoring interventions to meet the unique needs of each client, making the results more applicable and actionable.

In contrast, the other options do not align with the primary purpose of a line graph in this context. Illustrating data fluctuation without reference to objectives misses the essential aspect of goal-oriented practice. Showing averages over an extended period lacks the specificity that individual tracking provides, and displaying relationships between various variables without clarity undermines the direct evaluation of client outcomes that is central to single-case research designs.