Science:Math Exam Resources/Courses/MATH100/December 2016/Question 04 (c)
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Question 04 (c) 

Let be a continuous function defined for all real numbers . Suppose is increasing on the intervals and , decreasing on , and . How many zeroes does have? (i) 0 (ii) 1 (iii) 2 (iv) 3 (v) Cannot determine from the information given. 
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 

Draw graphs of functions satisfying the above conditions. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. On the interval the function increases to . However, we don't know whether the function passes the xaxis for , so we don’t have enough information to determine whether or not it crosses the axis. Answer: v 