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Infinitely many, since otherwise it could be a pattern that eventually breaks down and so not a pattern.
Since the x axis in infinite, the functions repeat infinitely many times.
why is it important to repeat an investigation several times?
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In general, as many times as you like. There is no limit to the number of times you can roll dice, for example. How many times you repeat a simulation depends on how precise you want to be with your results, and how much time you have.