MATH102 December 2016
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QB 1 • QB 2 • QB 3(a) • QB 3(b) • QB 3(c) • QB 4(a) • QB 4(b) • QB 4(c) • QB 5(a) • QB 5(b) • QB 6(a) • QB 6(b) • QB 7(a) • QB 7(b) • QB 7(c) • QB 8 •
Question A 03
Which of the following graphs is a sketch of the function for ?
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!
Check the asymptotes of the function.
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The function is not defined at ; it has a vertical asymptote at 0, because
so the first choice is out.
Now we check the behaviour of the function when .
First, note that has NO horizontal asymptote because , so the bottom left choice is out too. However, we see that , this means that as the function approaches to the line , in other words it has a slant asymptote at .
Answer: Top Right graph