Science:Math Exam Resources/Courses/MATH100/December 2012/Question 06 (e)
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Question 06 (e) 

FullSolution Problems. In questions 511, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 6. Let . Note that the domain of ƒ is the set of all nonzero real numbers; for example, . (e) Find all vertical asymptotes of the graph . 
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 

Check points of the function where it is not continuous and verify that one of the left or right hand limits are positive or negative infinity. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. As given in the original statement, the function has domain of all nonzero reals. The function itself is only not continuous at 0 so we check there for an asymptote. The value since this function when we plug in values of x slightly bigger than 0, the first term tends to 0 and the second term tends to positive infinity. Notice that the left hand limit is also positive infinity since the second term can be written as which is always positive. 