Functions
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The variable y is said to be a function of
x (an explicit
function), if to every value of x within a certain set of values there is one and
only one corresponding value of y. We write, y=f(x). Here, f is the name of the function. |
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The variable in a
function on which the value of the other variable depends. If y=f(x), x is the independent variable
and y is the
dependent one. |
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The set of values
the independent variable takes in a function. |
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The set of all
values the dependent variable may take corresponding to all values of the
independent variable. |
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If a function is
written in the form f(x,y)=0 and cannot be solved for
one variable in terms of another, we say that it is an implicit function in x and y. Here, if one of the two
variables takes a value, there may be more than one corresponding values for
the other variable. An example is:
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