Honors Pre-Calculus Appendix A1 Algebra Essentials

Objectives Work with sets Graph Inequalities Find Distance on the Real Number Line Evaluate Algebraic Expressions Determine the Domain of a Variable Use the Laws of Exponents Evaluate Square Roots Use a Calculator to Evaluate Exponents

Working with Sets

Examples of sets

Using Set-builder Notation

Intersection and Union

Finding the Intersection and Union of Sets

Sets of Numbers

Complex Numbers

Symbols for Number Sets

Closure A numerical set is said to be closed under a given operation if when that operation is performed on any element in the set the result of that operation is in that set. For example {x|x is even} is closed under addition because an even number plus an even number is even. {x|x is odd} is not closed under addtion because an odd number plus an odd odd number is not an odd number.

Closure Natural Numbers are closed under addition Integers are closed under addition and subtraction Rational and Real Numbers are closed under addition, subtraction, multiplication, and division (except 0). Complex numbers closed under addition, subtraction, multiplication, division (except 0), and taking roots.

Domain The set of values that a variable may assume is called the domain of the variable. The domain of the variable x in the expression is since if x=4 or x=-4 the denominator is not 0, so this expression is defined for all numbers.

Domain (continued) Example 2 The domain of the variable x in the expression is since if x=4 or x=-4 the denominator is not 0, so this expression is defined for all numbers.

Homework Pg A , 67-78