Conclusion

In this chapter, you began with an exploration of basic factoring. A review of factoring at this point is worthwhile because it anticipates work to come in the next chapter and also serves as an occasion for reviewing the basic properties of numbers. In this respect, it also proves worthwhile to briefly review the order of operations as you solve problems. Given this start, the discussion then turned to an extension of the previous explorations of sets. In this context, the focus of attention lay on showing that you can define relations between numbers by using sets.

A central notion in this respect is that of the domain and range of an ordered pair of numbers. Given a relation that generates ordered pairs, you can identify the first element of each ordered pair as belonging to a set you can designate as the domain. You can identify the second element as belonging to another set, the range. Relations lead to functions, which formalize the expression of the correspondence of the values you find in the domain and range of a relation. You can plot functions using a Cartesian coordinate system. After plotting the domain and range values of ordered pairs, you can apply the vertical line rule to it to determine whether the relation constitutes a valid function.