Science:Math Exam Resources/Courses/MATH110/December 2016/Question 01 (c)
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Question 01 (c) 

Find the range of . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Find the domain of given function first. 
Hint 2 

Recall the definition of the absolute value: positive values and zero stay the same, while negative values forget the minus sign and become positive. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. By Hint 1, we first find the domain of . Since it is a quotient function, is only defined when the denominator doesn't vanish, i.e., . For , we can write From Hint 2, we recall that when , and when . This means that when (note that we exclude the case here because it is in the denominator) and when . In other words, only takes the values and . Adding to it, we see that takes the values and . So the range of is the set .
Answer: the range of is . 