Many students find working with piecewise functions confusing and bewildering. Some calculus students may even cringe when they find out that understanding piecewise functions is very important for limits and, consequently, the rest of calculus.
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What makes piecewise functions so difficult to comprehend? 

1. Piecewise functions rely heavily on understanding domain. Many times students don't understand domain and instructors may not emphasize it.
2. You may have had it explained to you the first time by a teacher that really didn't understand it themselves.
3. Or the teacher may have understood it but may not have been able to communicate it well.
4. If you feel like math is something you cannot understand or do well in, your own mental block may keep you from understanding some topics, particularly difficult topics.
5. Some students think they can understand things without studying them and, therefore, when a more difficult topic comes up, they are lost because they don't spend the time outside of class learning it. Eventually, that mindset will come back to bite you, like when studying piecewise functions and especially later on in calculus. [ how to study calculus ]
Whatever the reason, it is time for you to take charge of your own learning and learn how to work with piecewise functions. I have helped many students come to understand this topic and they look at me and say, 'is that it?!' since they were surprised that they could now understand it.
Piecewise functions are not that hard and you can understand them too. Make sure you understand domain, explained on this page, and then go through the discussion on the piecewise functions page, working through the example. Then try your hand at a few practice problems on that page and see for yourself how easy it is. You will be glad you did when you get to limits in calculus.
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