Thinking about how changing audience, purpose, or context would change the rhetorical situation may give you ideas of how the current audience, purpose, and context affect the argument. However, you do not actually have to analyze what would happen if you were to change one of the variables, but fully investigate what effects each of the current variables has on the rhetorical situation. Try asking questions like these of your topic (there are more questions you may ask, these are just a few):

• Audience— who is the intended audience? what about secondary audiences? what ways best reach/influence this/these particular audience(s)? what beliefs do your audiences have about the topic? why do they have these beliefs? what influences on your audience cause them to believe certain things? what characteristics do they have that would affect how they feel about the topic? what sorts of concerns do they have? does the audience really know enough about the situation to make a decision?
• Purpose— what is the point of the argument: inform, persuade, sell, enlighten, create a debate over a topic, etc., or a combination of these? how can you achieve this purpose? does the audience understand both sides to the argument? do you want them to change their minds, or just consider a point of discussion? do they need to be informed before they can make a knowledgeable decision? do you need to do this?
• Context— in what setting is the argument percieved (where/how do people become involved with this topic)? how does the setting of the argument affect the presentation of its message? is the argument dependent upon anything from current events or other media (books, movies, political events, sports, etc.)? is the argument a part of another larger issue? (example: Stop Signs - do stop signs simply mean drivers should stop, or are they trying to achieve a higher purpose, such as creating order in a society)? what doesn't the audience know that is necessary to understand the topic?
  Remember that context is not only the setting, but more importantly, the issues surrounding the topic that influence the way people think about the topic.
  does the argument try to relate to an audience by incorporating or responding to any current events in any way?
• Combination of These— what particular tactics are necessary for the argument to achieve its purpose with a given audience (does the argument have to approach a topic carefully, is it a sensitive topic, etc.)? is the way the argument is presented (live speaker, magazine, tv, radio, etc.) affected by its particular audience?

Look for a good way to focus your analysis; you don't necessarily have to jump back and forth between audience, purpose, and context; try to focus your paragraphs; you might find that rather than organizing your paper by audience, purpose, and context, it may be easier to choose a component of the topic itself and show how that component is affected by the intertwining audience, purpose, and context, then choosing another component of the topic and doing the same, and so on.