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}
(0,2){\left(0 , 2 \right)}
(1,8){\left(1 , 8 \right)}
f:x↦4x2+2x+2for x∈R,0≤x<1.{f: x \mapsto 4 x^2 + 2 x + 2} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, 0 \leq x < 1.}
Df=[0,1).Rf=[2,8).\begin{aligned} D_f &= \left[0, 1\right). \\ R_f &= \left[2 , 8\right). \end{aligned}
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