Science:Math Exam Resources/Courses/MATH110/December 2010/Question 03 (c)
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Question 03 (c) 

Give an example of a function defined in the interval satisfying and , such that for any in . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The function you draw should have a discontinuity somewhere on its domain. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The simplest example of such a function would be the piecewise function:
The function is clearly defined on , but jumps from 1 to 1 at x = 0. Thus at no point in does . Two other variations:
In this case, the function is never equal to zero; however, we must add the point in the piecewise function to make it defined everywhere in our domain.
Here we have what would be a continuous function (the function x)  we've just removed the one point where it would equal zero and moved that point somewhere else, in this case, to . You could come up with many other piecewise functions using these same ideas. 