Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Absolute Values By Nana, Grade 11 Algebraic Definition • The absolute value of a number n is denoted |n| and is defined as follows: • If n 0, then |n| = n. • If n < 0, then |n| = -n. Algebraic Definition • The absolute value of a number is always positive. • For example: • Because 7 is positive, |7| = 7 • Because -5 is negative, |-5| = -(-5) = 5 Absolute Value and Distance • If n and b are real numbers, then |n – b| is the distance between n and b on the number line. Absolute Value and Distance • For example: • The number |3 + 4 | can be written as | 3 – (-4)|. • Thus, represents the distance between 3 and –4 on the number line. Absolute Value and Distance • Special case: • alternative definition of |c| • When b = 0, the distance formula shows that the distance from n to 0 is |n – 0| = |n| Geometric Definition • If n is a real number, then |n| is the distance from n to 0 on the number line. Geometric Definition • For example: • |5| denotes the distance from 5 to 0 on the number line, as shown below. Properties of Absolute Value • Let n and b represent real numbers. • 1. |n| 0 and |n| > 0 when n 0 • For example: • |19| = 19 19 0 • |0| = 0 0=0 Properties of Absolute Value • 2. |n| = |-n| • For example: • Let n = 2. Then |n| = |2| = 2 and |-n| = |-2| = 2. Therefore, |2| = |-2| Properties of Absolute Value • 3. |nb| = |n| |b| • For example: • Let n = 5 and b = -4 |nb| = |5 (-4)| = |-20| = 20 |n| |b| = |5| |-4| = 5 4 = 20 Therefore, |5 (-4)| = |5| |-4| Properties of Absolute Value • 4. |n/b| = |n| / |b|, where b 0 • For example: • Let n = -7 and b = 3 |n/b| = |-7/3| = |- 7/3| = 7/3 And |n|/|b| = |-7|/|3| = 7/3 Therefore, |-7/3| = |-7|/|3| Sources • Picture #1: http://www.sosmath.com/algebra/inequalities/pictures /pic15.gif • Picture #2: • http://www.showmethemath.com/Concepts_Explained /numberLineGifs/absPos5.gif • Pre-Calculus A Graphing Approach Book by Holt, Rinehart, and Winston End of presentation. Thank you.