Relation
Relation definition. Arelation between two sets is a collection of ordered pairs containing one object from each set. If the object is from the first set and the object is from the second set, then the objects are said to be related if the ordered pair is
Function
Function definition. A technical definition of afunction is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Ome-to-one function
A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1.
Into function
A function f from A to B is called onto if for all b in Bthere is an a in A such thatf (a) = b. All elements in Bare used.
One-to-one and onto deffinition
Remember that a functionis a set of ordered pairs in which no two ordered pairs that have the same first component have different second components. This means that given any x, there is only one y that can be paired with that x.
Onto Function
A function
Domain
The set of values of the independent variable(s) for which a function or relation is defined. Typically, this is the set of x-values that give rise to real y-values. Note: Usually domain meansdomain of definition, but sometimes domain refers to a restrict
Range
Range (statistics) The difference between the lowest and highest values. In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 ? 3 = 6. Range can also mean all the output values of a function.
Discrete relation
A relation is any association or link between elements of one set, called the domain or (less formally) the set of inputs, and another set, called the range or set of outputs.
Continuous relation
A function to represent a graph which has no gaps, breaks or holes is called continuous function.
Formula :
A function f(x) is said to be continuous at a point of 'a' if the following conditions are satisfied, 1) f(a) is defined, 2) limx->a f(x) exist, 3)
Vertical line test
In mathematics, thevertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
Independent variable
Independent variable definition. Anindependent variable is avariable that represents a quantity that is being manipulated in an experiment. A dependentvariable represents a quantity whose value depends on those manipulations.
Dependent variable
In mathematics, avariable whose value is determined by the value of an independentvariable. For example, in the formula for the area of a circle, A = ?r2, A is the dependent variable, as its value depends on the value of the radius (r). Compare independen
Function notation
Function notation is a system of symbols used in mathematics, but it is arguably much easier to learn than musical notation. Function notation is an efficient and effective way to display functions of all types in mathematics.
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