Science:Math Exam Resources/Courses/MATH110/April 2013/Question 01 (d)
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Question 01 (d) 

Determine whether the following statement is true or false. If it is true, provide justification. If it is false, provide a counterexample. (d) If ƒ has a vertical asymptote at x = 0, then is reciprocal 1/ƒ has a vertical asymptote at x = 0. 
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 

Try known examples of functions with vertical asymptotes at 0 and look at their reciprocal functions. This should give you the intuition of this question. One can also look at this abstractly by recalling the definition of what it means to have a vertical asymptote and how this would affect the reciprocal function, but trying examples should be sufficient. 
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. This statement is false. As a counterexample, consider ƒ(x) = 1/x. It has a vertical asymptote at x = 0, but its reciprocal 1/ƒ = x has no vertical asymptotes. 