# Function

A real function of real variables is any function, f, that associates to each element of a certain subset (domain), another real number (image).

f : D

x      f(x) = y

The subset which defines the function is called the domain.

The number x belonging to the domain of the function is called the independent variable.

The number, y, associated for f to the of value x, is called the dependent variable. The image of x is designated by f(x):

y = f(x)

The range of a function is the set of real values that takes the variable y or f(x).

x

Initial set Final set

Domain Range

The domain is the set of elements that has an image.

D = {x /f (x)}

The range is the set of the images.

R = {f(x)/x D}

### Graph of a Function

If f is a real function, every pair (x, y) = (x, f(x)) determined by the function f corresponds to the Cartesian plane as a single point P(x, y) = P(x, f(x)). The value of x must belong to the domain of the definition of the function.

The set of points belonging to a function is unlimited and the pairs are arranged in a table of values which correspond to the points of the function. These values, on the Cartesian plane, determine points on the graph. Joining these points with a continuous line gives the graphical representation of the function.

 x f(x) 1 2 3 4 5 2 4 6 8 10

#### Example

The price of a taxi ride is represented by: y = 3 + 0.5x. Where x is the time in minutes of the ride.

 x y= 3 + 0.5x 10 20 30 8 13 18

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