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Graphs and Functions
Domain and range

A function is a set of ordered pairs of real numbers in which no two ordered pairs have the same first component.

An example of function according to this definition is
f = {(1,2),(2,3),(3,4),(4,5)(5,6)}

The equation f(x)=y, read as "f of x equals y" is special notation for functions to indicate that the ordered pair, (x,y) is in the function.

The domain of a function is the set of all first components of the ordered pairs in the function. The range is the set of all second components of the ordered pairs.

Find the domain and range of the function:
f = {(1,2),(2,3),(3,4),(4,5)(5,6)}

Domain={1,2,3,4,5}
Range={2,3,4,5,6}

Find the domain and range:

 x y -1 -4 -2 -8 -3 -12 -4 -16
Domain = {-1,-2,-3,-4}
Range = {-4,-8,-12,-16}

Many times a function is given by a graph:

Find the domain and range: Domain = {-1,0,2} Range = {-2,2-1}

Many times a function is given by the rule that generates the ordered pairs, rather than by the ordered pairs themselves (for example f(x)=x2). The domain in this case should always be chosen to be the largest set of real numbers for which the defining rule makes sence (no division by 0 or square roots of negative numbers,..)

Find the domain and range: f(x)=x2

Domain of f = All real numbers.
Range of f = {y/y≥0}

Find the domain and range: g(x)=

Domain of f = {x/xєR and x≠2}
Range of f = {y/yєR and y≠0}