Let R be the relation on the set of all human beings (not just those in your family) defined by x R y if and only if x is a parent of y. a. If x is you, describe the set of people fy W x R yg. b. If y is you, describe the set of people fx W x R yg. c. Determine which of the following properties is satisfied by R: reflexive, irreflexive, symmetric, antisymmetric, transitive. d. Describe R1 .

Math 1311 Section 1.2 Functions Given by Tables Sometimes we work with functions for which we do not know a formula. In this case, many times we use a table of values to show the value of the function for specific values of the independent variables. Why tables Advantages Tables are how we can organize experimental data for which the relationship is not known in formula form. Tables provide an easy to see relationship between quantities, since evaluating a formula is not always easy. It is often easier to spot trends in tabular data. Disadvantages There are only finitely many values of the function known; we do not necessarily know what happens in the gaps. To use the table to guess what will happen in the future, you must assume that there is a pattern and that it will continue. Average Rate of Change is a ratio of the change in function values to the change in values of the independent variable. Average rate of change of a function over the interva1 2is defined to be )2 − ( 1 = − 2 1 And AROC has units: the units of divided by the units of the variable. This is a VERY IMPORTANT concept throughout this course. Limiting Values Information about physical situations can sometimes show that limiting values are