Science:Math Exam Resources/Courses/MATH110/December 2010/Question 06 (a)
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Question 06 (a) 

A circle of radius 5 centered on the origin has the equation This circle is not a function. Why not? 
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 a relation to be a function, how many yvalues can be associated with a single xvalue? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Given a relation or rule that takes input values (usually denoted x) and produces output values (usually denoted y), the relation is a function if each xvalue is associated with only one yvalue. In other words, the graph of the relation must pass the "vertical line test"  if you can draw a vertical line that intersects the graph at two points, the relation is not a function. In this case, a single xvalue in the domain will be associated with two yvalues from the upper and lower half of the circle. This is the same as saying that a circle fails the vertical line test, as a vertical line drawn through any point in the domain will intersect the graph in two places. 