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Precalculus: Functions

Terms

Functions

Sets and Relations

Cartesian Product  -  The set of all possible ordered pairs (a, b) composed of elements taken from the two sets, A and B .
Composition  -  A function operation symbolized (f o g)(x) that is equivalent to f (g(x)) .
Defined  -  A function is defined at a given value of the independent variable if it assigns that input an output; defined means "takes on a value".
Dependent Variable  -  The output variable of a function; the variable whose value depends on the input, or independent variable.
Domain  -  The set of all inputs for which a function or relation is defined.
Even Function  -  A function f is even if f (x) = f (- x) .
Function  -  A relation which assigns exactly one element in its range for each element in its domain.
Horizontal Line Test  -  The test by which it is shown whether a function is a one-to-one function or not, and therefore whether its inverse is a function.
Independent Variable  -  The variable of a function which does not depend on the other variable -- it is the input.
Inverse  -  A relation which assigns a correspondence from the elements of the range to those of the domain. The inverse of a function or relation can be found by interchanging the variables in the function or relation.
Odd Function  -  A function f is odd if f (x) = - f (- x) .
One-to-One Function  -  A function is one-to-one if each element in its range is paired with exactly one element from its domain.
Periodic Function  -  A function is periodic if and only if f (x) = f (x + c) , for all values x , where c is a constant. A periodic function repeats itself at regular intervals.
Piecewise Function  -  A function is piecewise if and only if it uses different rules for different parts of its domain.
Range  -  The set of all outputs of a function or relation.
Relation  -  A rule that associates the elements of one set with those of another set. A relation can also be thought of as all of the ordered pairs which satisfy the rule.
Undefined  -  A function is undefined at a given value of its independent variable if for that value, there is no output--this occurs when a particular input creates a situation in which there is division by zero, or an even root of a negative number, for example.
Vertical Line Test  -  The test by which a relation is either shown to be a function or not. The graph of a function does not intersect with a vertical line more than once.

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