Calculus- Function definitions Flashcards

Terms Definitions
Definition of a Function
A function f is a rule that assigns to each element x in a set D exactly one element, f(x), in a set E.
Domain
All possible inputs that make a function true (all x inputs)
Range
All possible output values of f(x) that make the function true. (all y values)
Independent Variable
A symbol that represents an arbitrary number in the domain of a function f.
Dependent Variable
A symbol that represents a number in the range of f.
Vertical line test
A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once.
Piecewise defined Functions
Defined by different formulas in different parts of their domains.
Even Function
A function f that satisfies f(-x)=f(x) for every number x in its domain.
Odd Function
Function f satisfies f(-x)= -f(x) for every number x in its domain.
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