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Absolute value function

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Algebra and Trigonometry

Definition

An absolute value function is a piecewise function that describes the distance of a number from zero on the number line, without considering direction. It is typically written as $f(x) = |x|$, where $|x|$ denotes the absolute value of $x$.

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5 Must Know Facts For Your Next Test

  1. The domain of an absolute value function is all real numbers ($\mathbb{R}$).
  2. The range of an absolute value function is all non-negative real numbers ($[0, \infty)$).
  3. The graph of an absolute value function forms a 'V' shape with its vertex at the origin (0,0).
  4. Absolute value functions can be expressed as piecewise functions: $ f(x) = x $ if $x \geq 0$ and $ f(x) = -x $ if $x < 0$.
  5. Transformations such as shifts, reflections, and stretching/compressing apply to absolute value functions similarly to other types of functions.

Review Questions

  • What are the domain and range of the absolute value function?
  • How does the graph of an absolute value function look?
  • Express the absolute value function as a piecewise function.
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