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# Functions

### Introduction to functions terms (Algebra I)

Term | Definition |
---|---|

Dependent Variable (quantity) | a variable whose value depends upon input; what is being evaluated in a mathematical equation |

Independent Variable (quantity) | a variable that is manipulated to determine the value of a output; the value or quantity being inputted into an equation |

Input | the value or quantity being used to calculate/evaluate an equation |

Output | the value given from an equation after a calculation has been performed/executed |

Function | a special type of relation that pairs each domain value with exactly one range value (the x-values cannot repeat) |

Nonlinear | data that does not have a linear patern |

Representation | a table, graph, equation, verbal are the different representations possible for any given relation or function |

Continuous graph | graphs made with a connected line or curve |

Discrete graph | a graph where data is only represented by coordinate points (dots) |

Linear Function | a function whose graph is a line with a constant rate of change and the direction of line does not change |

Domain | in a relation, the set of first coordinates (or x-values) of the ordered pairs; all the x-values for a given relation or function; the input |

Range | in a relation, the set of second coordinates (or y-values) of the ordered pairs; all the y-values for a given relation or function; the output |

Relation | a set of ordered pairs |

Vertical Line Test | draw vertical lines over a graph and if the lines only intersect the graph once, it is a function. If any lines intersect the graph more than once, it is not a function |

Function Notation | In a function, if "x" is independent and "y" is dependent, the function notation for "y" is "f(x)" - read "f of x". When you see function notation, it signals that the equation and resulting relation is a function. |

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