# 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 < 5 | means that x can be every number smaller than 5. |

x ≥ –7 | means that x can be every number greater than or equal to –7. |

3 ≤ x ≤ 8 | means 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 < 0 | means 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 < 8 | means 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 ≠ –7 | means 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 = 3x^{2}– 2 |
every x |
y ≥ –2 |
See graph |

y = |
x ≥ –2 |
y ≥ –4 |
See graph |

y = |
x ≠ 3 |
y ≠ 1 |
See graph |

y = |
x ≤ –4 of x ≥ 4 |
y ≥ 3 |
See graph |

y = |
–4 ≤ x ≤ 4 |
3 ≤ y ≤ 7 |
See graph |

At square root relation you can find another three examples.