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We learned about graphing Piecewise functions in math class today. And to be honest with you, I found it incredibly confusing. I find the most trouble in finding a place to start and knowing whether or not the circles should be open circles or closed circles.

For Example: Jennifer is completing a $15.5$ mile triathlon. She swims $0.5$ miles in $30$ minutes, bicycles $12$ miles in $1$ hour and runs $3$ miles in $30$ minutes. Write a Piecewise function for the distance Jennifer travelled compared to the time and graph it.

I'm just not too sure where to begin and any ideas on what to do in this kind of problem?

Frank
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    You have my deepest sympathy. In so far as I understand it, the pedagogical concept of so-called "piecewise functions" is utterly demented. Your confusion about the open or closed circles is quite understandable. The logical form of the question you quote is essentially the same as that of "Jennifer is a banana. Write down an equation and then draw its graph." – Rob Arthan Sep 28 '16 at 22:46
  • Are those the exact directions? – Display Name Sep 28 '16 at 22:51
  • @Display Name Yes. Write a Piecewise function for the problem, then graph it. I have a hard time just graphing the function in general and finding a place to begin writing your function. I have a test over this stuff tomorrow too... D: – Frank Sep 28 '16 at 22:54
  • @RobArthan Man, Piecewise functions are really confusing. D: – Frank Sep 28 '16 at 22:54
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    As Rob Arthan points out the question is badly worded. They probably want the function to describe The distance travelled by Jennifer at any time t, but the way it reads you can pick any piece wise defined function and graph it. – Display Name Sep 28 '16 at 23:02
  • @Frank: yes. The notion of a piecewise continuous function is quite straightforward, but modern teaching theory seems to have chosen to replace itwith something called a "piecewise function" that has no agreed mathematical meaning. – Rob Arthan Sep 28 '16 at 23:03
  • @DisplayName: yes, but the part of the OP's question about "open circles" and "closed circles" seems to be a confusion wired in from a misinformed and demented notion of how piecewise continuous functions work. The pedagogue who thought a notion of "piecewise function" was useful should have his or her ears stabled to the topologist's sine curve. – Rob Arthan Sep 28 '16 at 23:08
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    I concur with all the comments about how bad this question is. That said, just draw the graph with time for the x axis and y axis for the distance covered. It will start at (0,0) and consist of segments of straight lines, with slopes determined by her rate for each leg. The segments will meet, so there are no "open" or "closed" circles. (The right name for this particular function is "piecewise linear"). When you're done you can answer your own question here and folks will upvote it. – Ethan Bolker Sep 29 '16 at 00:07
  • @Ethan Bolker How about if I just change the question to something more relevant? – Frank Sep 29 '16 at 00:19

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