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Range

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College Algebra

Definition

The range of a function is the set of all possible output values it can produce. It corresponds to the y-values in the coordinate plane.

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5 Must Know Facts For Your Next Test

  1. The range depends on the domain of the function and its rule.
  2. For a quadratic function $f(x) = ax^2 + bx + c$ with $a > 0$, the range is $[k, \infty)$ where $k$ is the vertex's y-coordinate.
  3. If a function has no restrictions, like polynomials of odd degree, its range is all real numbers ($\mathbb{R}$).
  4. The range can be determined by solving for y in terms of x or analyzing the graph of the function.
  5. In piecewise functions, each piece contributes to the overall range.

Review Questions

  • What is the range of the function $f(x) = x^2 - 4$?
  • How does one determine the range of a rational function?
  • Explain how to find the range from a given graph.

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