A piecewise is defined by multiple sub-functions, each applying to a certain interval of the main functions domain. It makes sense to me to call this function piecewise because it has two different kind of functions that I think share the same domain and range when it is applied correctly. When I moved the purple dot from left to right I began to realize a change in both functions. I also realized that there was a difference when there was either a concave up or concave down graph.

**End your blog post with a** **question**: Why do you guys think that it varies when the graph has a concave upward or downward parabola? And how do you think they are used in real life ?

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I can answer your second question. In real life, piecewise functions are used when companies have a discounted rate if you buy a lot of their product. For example, phone companies sometimes charge a flat rate of say $80/month unless you use more than a certain amount of data (say 5GB.) At that point, you are charged by the GB of data and so you would have a different formula if x > 5. Does that make sense?

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