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}
(1,11){\left(1 , 11 \right)}
(3,41){\left(3 , 41 \right)}
f:x↦4x2−x+8for x∈R,1≤x<3.{f: x \mapsto 4 x^2 - x + 8} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, 1 \leq x < 3.}
Df=[1,3).Rf=[11,41).\begin{aligned} D_f &= \left[1, 3\right). \\ R_f &= \left[11 , 41\right). \end{aligned}
Next: Inverse functions >>