Math Interactive
2. Functions
2.1. Basics
2.1.2. Domain and range
Important

The range is the set of all possible outputs (”yy“-values) of a function.

We denote the range of a function ff by RfR_f.

Graphs are especially useful to determine the range of a function.
End points, turning points and asymptotes are important in determining the range.

Examples

Use the following to generate functions and observe how their range can be determined from the graph.

0
x{x}
y{y}
(−1,−3){\left(-1 , -3 \right)}
(1,−3){\left(1 , -3 \right)}
(0,−2){\left(0 , - 2 \right)}
f:x↦−x2−2for x∈R,−1<x≤1.{f: x \mapsto - x^2 - 2} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -1 < x \leq 1.}
Df=(−1,1].Rf=(−3,−2].\begin{aligned} D_f &= \left(-1, 1\right]. \\ R_f &= \left( -3, - 2\right]. \end{aligned}
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