Range

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.

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.

Related terms

Domain: The set of all possible input values (x-values) for which a function is defined.

Function: A relation between sets that associates every element of a first set to exactly one element of a second set.

Inverse Function: A function that reverses another function; if $f(x)$ maps x to y, then its inverse $f^{-1}(y)$ maps y back to x.