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}
−2{- 2}
(−4,−6){\left(-4 , -6 \right)}
(−2,0){\left(-2 , 0 \right)}
f:x↦3x+6for x∈R,−4≤x≤−2.{f: x \mapsto 3 x + 6} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -4 \leq x \leq -2.}
Df=[−4,−2].Rf=[−6,0].\textstyle \begin{aligned} D_f &= \left[-4, -2\right]. \\ R_f &= \left[ -6, 0 \right]. \end{aligned}
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