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# Functions

### A review of the vocabulary associated with mathematical functions

Relation A mathematical relationship between quantities
Function A rule of correspondence that matches each item from one set with exactly one item from another set.
Domain The set of all possible inputs for a function
Range The set of all possible outputs for a function
Inverse of a Function Acts like an "Undo" function. If your function mapped 2 to 5, this would map 5 back to 2.
Opposites x and -x
Reciprocals x and 1/x
One-to-one function Each input corresponds to only one output and each output to only one input. The input and output are "married".
Recursive Function This type of function defines the value of an output in terms of prior outputs. It refers back.
First Differences Found by subtracting consecutive terms in a sequence. If these are all equal, the sequence has a linear model.
Second Differences Are found by subtracting consecutive first differences. If these are all equal, the sequence has a quadratic model.
Compound or Piece-wise Defined Function A function that has different rules that apply for different types of inputs.
Composition of Functions To arrange functions in a specific order. For example: First plug into f, then plug your result into g.
Dependent Variable A quantity whose value is based upon the value of another quantity.
Created by: bretschj