## 8.1. Pointwise Convergence

### Example 8.1.2 (b): Function Family Example

Consider

*{ f*, where_{n}(x) } = {^{n}/_{(x - n)}}*n*is a natural number. What is the domain of this family? What is the parameter set?If *f _{n}(x) = ^{n} / _{(x - n)}* then clearly

*x # n*for each

*n*. Thus, the domain for the family

*{ f*is

_{n}}*, i.e. all real numbers except for the positive integers.*

**R / N**Here are a few members of this family (click on *Options* to plot a
few more). Note that *f _{n}(0) = -1* for all

*n*.

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