Final answer:
Line, pie, and bar graphs provide the most control over the data narrative, each serving specific purposes. However, graph manipulation can alter perceptions, necessitating careful construction.
Step-by-step explanation:
The type of visualizations that give you the most control over the story you want to tell with your data are line graphs, pie graphs, and bar graphs. Each of these graphs allows for different perspectives and emphasis on the data presented. Line graphs are ideal for showing trends over time, pie graphs are best for illustrating proportions of a whole, and bar graphs are suitable for comparing different groups.
However, it is important to be aware that these graphs can be manipulated to alter viewers' perceptions of the data, for instance, by adjusting the scale or the time frame. Thus, it is crucial to make thoughtful decisions about these elements to maintain the integrity of the story the data is telling.