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Mathematics LibreTexts

2.6: Absolute Value Functions

  • Page ID
    203395
    • Roy Simpson, Cosumnes River College
    • OpenStax

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    Prerequisite Skills
    • Arithmetic
      • The Absolute Value of a Number
    • Absolute Value Functions
      • The Concept of Absolute Value

    Focus on Calculus - Piecewise Definition of the Absolute Value

    Definition: Absolute Value Function

    The absolute value function is defined to be \( f(x) = |x| \), where\[ |\blacksquare| = \begin{cases}
    \blacksquare, & \text{ if } \blacksquare \geq 0 \\[6pt]
    -\blacksquare, & \text{ if } \blacksquare < 0 \\[6pt]
    \end{cases} \nonumber \]

    MyOpenMath \(\PageIndex{15}\)

    Graphing an Absolute Value Function

    MyOpenMath \( \PageIndex{ 9 } \)

    Solving an Absolute Value Equation

    Definition: Absolute Value Equation

    An absolute value equation is an equation in which the unknown variable appears within the absolute value bars.

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    MyOpenMath \( \PageIndex{ 11 } \)

    Focus on Calculus - Solving Absolute Value Inequalities

    Definition: Absolute Value Inequality

    An absolute value inequality is an inequality in which the unknown variable appears within the absolute value bars.

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    This page titled 2.6: Absolute Value Functions is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Roy Simpson, Cosumnes River College (OpenStax) via source content that was edited to the style and standards of the LibreTexts platform.