Science:Math Exam Resources/Courses/MATH102/December 2015/Question 09
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Question 09 

Match the function ((a), (b), (c)) to its sketch (one of (D), (E), (F), (G)). (a) , (b) (c) 
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 

For each given function, consider the function value at , the limit at infinity , and the sign of the function on the interval . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. (a) Let . Since , the graph (G) is out. Considering , the graph (E) is also out. Finally, we can factor out the numerator and rewrite as . Then, for , the denominator of the fraction is positive , and so is the numerator . It follows that for , , and hence (F) is out. To sum, it matches with (D). (b) Let . Using and , as in the solution for (a), the graphs (G) and (E) are out. But for , we have and , which implies that . i.e., (D) is out. Therefore, it matches with (F).
We can easily see that and . Then, (D), (F), and (G) are out, so that it matches with (E) Answer 