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2.1 Absolute Value Equations and Functions

Understanding absolute value equations, inequalities, and their V-shaped graphs with transformations.

本节包含的知识点

  • 2.1.1 Absolute Value Equations — Solving equations containing absolute value expressions using algebraic methods and case analysis.
  • 2.1.2 Absolute Value Inequalities — Solving and graphing inequalities with absolute value, including compound inequalities and interval notation.
  • 2.1.3 Absolute Value Functions and V-shaped Graphs — Understanding the parent function f(x) = |x| and its characteristic V-shaped graph with vertex and symmetry properties.
  • 2.1.4 Transformations of Absolute Value Functions — Applying translations, reflections, and stretches to absolute value functions and analyzing their effects on the graph.
  • 2.1.5 Piecewise Functions and Absolute Value — Expressing absolute value functions as piecewise-defined functions and analyzing their behavior on different intervals.