Science:Math Exam Resources/Courses/MATH110/December 2014/Question 03 (a)
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Question 03 (a) 

Sketch the graph of the following function, 
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 

Sketch the graph of each piece separately, i.e. an exponential function, a line and a square root function. For each graph keep the piece that satisfies the given interval. 
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. For , has horizontal asymptote because of , is increasing and passes though . On the other hand, for , the graph of is a piece of parabola which satisfies , , and . Finally, for , the graph of is a straight line passing through . Based on this information, we can draw the graph of as follows; 