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,−12){\left(1 , -12 \right)}
(−27,−37){\left(- \frac{2}{7} , - \frac{3}{7} \right)}
f:x↦−7x2−4x−1for x∈R,x<1.{f: x \mapsto - 7 x^2 - 4 x - 1} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x < 1.}
Df=(−∞,1).Rf=(−∞,−37].\begin{aligned} D_f &= \left(-\infty, 1\right). \\ R_f &= \left(-\infty, - \frac{3}{7}\right]. \end{aligned}
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