Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (c)
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Question 01 (c) 

Determine whether the following statement is true or false. If it is true, provide justification. If it is false, provide a counterexample. c) is continuous at all real numbers. 
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 

You need to check three things: 1. That the function is continue at the break point given by 2. That the right hand side of the function is continuous at all points larger than 1. 3. That the left hand side of the function is continuous at all points smaller than 1. 
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. False: To hunt for discontinuities, we have to check inside each piece and also at the boundary.
That means is NOT continuous over all real numbers. 