Rewrite without using the absolute value symbol. (a) |4-π| (b) |π-4| |c||√(2)-1.5|

Name: Problem 3, Chapter 1: Calculus
Uploaded: 2022-03-04T20:57:20-08:00
Duration: 2 min 58 s
Channel: Eleni Katirtzoglou
Description: Rewrite without using the absolute value symbol. (a) |4-π| (b) |π-4| |c||√(2)-1.5|

step 1 Hi over here we would like to rewrite these three expressions without using the absolute value r

Rewrite without using the absolute value symbol. (a) |4-π|...

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Key Concepts

Absolute Value Function

The absolute value function measures the non-negative distance of a number from zero. It converts any real number into its magnitude regardless of its sign and is foundational for understanding the process of rewriting expressions from a format that uses the absolute value symbol to one that is piecewise defined.

Piecewise Definition of Absolute Value

Rewriting expressions without the absolute value symbol typically involves the piecewise definition: for any real expression a, |a| equals a when a is non-negative and -a when a is negative. This method is essential when adapting an expression to reveal its behavior based on the sign of its components.

Properties of Absolute Values in Products

When dealing with products that involve absolute values, properties like |ab| = |a||b| are key. These properties allow for the distribution and reconfiguration of absolute value operations across factors, thereby simplifying the transformation of expressions into forms that do not explicitly use absolute value notation.

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