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Reasoning: Can a function have an infinite number of values in its domain and only a finite number of values in its range? If so, describe a real-world situation that could be modeled by such a function.

Writing: What is the difference between a relation and a function? Is every relation a function? Is every function a relation? Explain.

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asked by Macie
  1. Sure. Consider a step function.
    [x] is the greatest integer less than or equal to x.

    For example,

    [1.3] = 1
    [1.9] = 1

    Now consider the domain as the interval [1,2]

    The domain is the whole interval, with infinitely many values, but the range is a single value: y=1

    Such a step function could describe the position of a ratchet on a gear. The angle varies continuously, but the ratchet assumes only a finite number of positions.

    A relation is just a set of value pairs, relating each first value to the second value.

    The relation is a function only if no two first-values are related to the same second-value.

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    posted by Steve

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