Interactive Real Analysis - part of

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Example 8.1.2 (b): Function Family Example

Consider { fn(x) } = { n / (x - n) }, where n is a natural number. What is the domain of this family? What is the parameter set?

If fn(x) = n / (x - n) then clearly x # n for each n. Thus, the domain for the family { fn } is R / N, i.e. all real numbers except for the positive integers.

Here are a few members of this family (click on Options to plot a few more). Note that fn(0) = -1 for all n.

The parameter set for our family is specified to be the set of natural numbers.

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