Stitz-Zeager_College_Algebra_e-book

# Every point on the graph of f is simultaneously a

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: rem 2.1. Properties of Absolute Value: Let a, b, and x be real numbers and let n be an integer.a Then • Product Rule: |ab| = |a||b| • Power Rule: |an | = |a|n whenever an is deﬁned • Quotient Rule: a |a| = , provided b = 0 b |b| • |x| = 0 if and only if x = 0. • For c > 0, |x| = c if and only if x = c or x = −c. • For c < 0, |x| = c has no solution. a Recall that this means n = 0, ±1, ±2, . . . . The proof of the Product and Quotient Rules in Theorem 2.1 boils down to checking four cases: when both a and b are positive; when they are both negative; when one is positive and the other 128 Linear and Quadratic Functions is negative; when one or both are zero. For example, suppose we wish to show |ab| = |a||b|. We need to show this equation is true for all real numbers a and b. If a and b are both positive, then so is ab. Hence, |a| = a, |b| = b, and |ab| = ab. Hence, the equation |ab| = |a||b| is the same as ab = ab which is true. If both a and b are negative, then ab is positi...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online