Formulas, graphs & relations » Domain and range

General

Symbols

< means smaller than
> means greater than
≤ means smaller than or equal to
≥ means greater than or equal to
∞ means infinite
≠ means not equal to

Interval

An interval relates to a certain part of the number line.

x < 5means that x can be every number smaller than 5.
x ≥ –7means that x can be every number greater than or equal to –7.
3 ≤ x ≤ 8means that x can be every number greater than or equal to 3, but smaller than or equal to 8. (x lies between or is equal to 3 and 8)
–2 ≤ x < 0means that x can be every number greater than or equal to –2, but smaller than 0. (x lies between –2 and 0 or is equal to –2)
3 < x < 8means that x lies between 3 and 8.
x < 3 or x ≥ 8 means that x can be every number smaller than 3 or greater than or equal to 8.
x ≠ –7means that x can be every number, except –7.

Other notations

There is more than one way to note down intervals:

Interval notation
Inequality Netherlands US/UK Belgium
x < 5 ⟨←, 5⟩ (–∞, 5) ]–∞, 5[
x ≥ –7 [–7, →⟩ [–7, ∞) [–7, ∞[
3 ≤ x ≤ 8 [3, 8] [3, 8] [3, 8]
–2 ≤ x < 0 [–2, 0⟩ [–2, 0) [–2, 0[
3 < x < 8 ⟨3, 8⟩ (3, 8) ]3, 8[
x < 3 or x ≥ 8  ⟨←, 3⟩ or [8, →⟩ (-∞, 3) or [8, ∞) ]-∞, 3[ or [8, ∞[
x ≠ –7 ⟨←, -7⟩ or ⟨-7, →⟩ (-∞, -7) or (-7, ∞) ]-∞, -7[ or ]-7, ∞[
every x ⟨←, →⟩ (–∞,∞) ]–∞, ∞[

Help: I see squares instead of symbols at the Dutch notation. Click here.

Domain

The domain of a formula consists of all possible values of x for which the formula has an outcome for y.

Range

The range of a formula consists of every possible outcome, so every possible value of y.

Examples

You can show the graph for each formula by clicking on 'See graph'. The graph will appear underneath the table.

Formula Domain Range
y = 3x + 5 every x every y See graph
y = 3x2– 2 every x y ≥ –2 See graph
y = -4 + square root(x+2) x ≥ –2 y ≥ –4 See graph
y = 1 + 3/(x-3) x ≠ 3 y ≠ 1 See graph
y = 3 + square root(x^2 - 16) x ≤ –4 of x ≥ 4 y ≥ 3 See graph
y = 3 + square root(16 - x^2) –4 ≤ x ≤ 4 3 ≤ y ≤ 7 See graph

At square root relation you can find another three examples.