First of all, what is a function? A function, or a mapping, is kind of like an infernal machine, a system which is a little complicated though logical,
something abstract enough at the beginning, in short a sort of creature, to whom you give a number and comes out with another number.
For example for the function f(x) = 2x + 3, if you give it 5, you will get
.
If you give it 10, it will give you back f(10) = 23, if you give it (-4) you will have (-5), if you give it 0,5 you will have 4.
There are many functions, ,
, and even : |

For each value of x on the horizontal axis (the x axis), you can calculate the value of the corresponding f(x). |

Concerning the function f(x) = 2x+3, if you have x = 1 you have also f(x) = 5. You make a small cross at 1, the abscissa of the point, and 5 for the y axis (at point 5 for the height), that is to say here : |

In the case of our function f(x)=2x+3, its graphic representation is a straight line. In fact, all the linear functions are represented by straight lines.

Number b which is in the expression of the function is called y-intercept (or ordinate at origin). It is equal to the height at which the straight line cuts the y axis (the vertical axis). In the case of our function, b=3 (yellow point).

Finally, if you know the coordinates A and B of two points on a straight line, you can calculate the slope of this straight line. You must use the following formula: