Science:Math Exam Resources/Courses/MATH110/April 2013/Question 02 (b)
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Question 02 (b) 

Sketch a single function satisfying all of the listed criteria. 
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 

What does it mean when a limit evaluates to a number? To infinity? Each limit listed above turns into a graph feature like a point or asymptote. 
Hint 2 

Each limit translates into the following graph feature:

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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. See the second hint for how each limit translates into a feature of the graph.
There is a lot of freedom in how your graph may look, but as long as you follow the key points above your graph will be correct. Below is our example (the purple lines represent asymptotes): 