In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x2, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.
Thus we have two quantities (called "variables") and we observe that there is a relationship between them. If we find that for every value of the first variable there is only one value of the second variable, then we say: "The second variable is a function of the first variable."
The first variable is the independent variable (usually written as x), and the second variable is the dependent variable (usually written as y).
The domain of a function is the set of all possible x-values which will make the function work and will output real y-values.
The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.
The following applet shows the graph of sine function. Its domain ( which can be tracked by point B) and range(which can be tracked by point C) are respectively (-∞ , ∞) and [-1,1].
Thus we have two quantities (called "variables") and we observe that there is a relationship between them. If we find that for every value of the first variable there is only one value of the second variable, then we say: "The second variable is a function of the first variable."
The first variable is the independent variable (usually written as x), and the second variable is the dependent variable (usually written as y).
The domain of a function is the set of all possible x-values which will make the function work and will output real y-values.
The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.
The following applet shows the graph of sine function. Its domain ( which can be tracked by point B) and range(which can be tracked by point C) are respectively (-∞ , ∞) and [-1,1].
