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Question 491908: Please explain why this is a function. "A rule that associates, to a given time, the distance from a swinging pendulum to its lowest point"
Found 2 solutions by richard1234, ccs2011:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! For some given time, the distance from the pendulum to its lowest point is uniquely defined, i.e. there is one "output" for each input (time). Hence we can say that this is a function.
Answer by ccs2011(207)  (Show Source):
You can put this solution on YOUR website! This is a function because for every point in time there is only one corresponding distance. For instance, there is no point in time where the pendulum is 2 different distances from lowest point.
The function is not one-to-one because the pendulum will swing back and forth so have different times correspond to the same distance.
If you map out the points, it will start at 0 then increase to a vertex, then go back down to 0, then goes up again...and so on.
By drawing it out, you will see it passes the vertical line test.
More specifically, the function will look like the sine function.
Hope that helps
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