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 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| f(x) | 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 | 10 | 20 | 30 |
|---|---|---|---|
| y= 3 + 0.5x | 8 | 13 | 18 |
