# 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 |