Linear Functions

What is a linear function?

A linear function is a first degree polynomial function and a particular case of the affine function f(x) = a.x + b, where b = 0. A linear function is a function of f : ℝ→ℝ defined as f(x) = a.x, where a is a real number and a ≠ 0. 

The a number that multiplies by x, is called the coefficient of the function. When the coefficient = 1, the linear function will be called as the identity function, f(x) = x

What is the linear function graph?

The graph of a linear function is a straight line that crosses the origin, thus, the point (0, 0). The a coefficient indicates the slope or steepness of the line. The higher a coefficient, the more steep the graph line will be.

Linear functions can be increasing or decreasing. To know this, one just has to identify the signal of the a coefficient. If a is positive, the function will be increasing. If a is negative, the function will be decreasing.

How to graph linear functions?

To plot the graph of a linear function, it is necessary to know, at least, two points. One of the points is (0, 0) and the other point can be calculated, as the following example:

Given the function f(x) = 2.x

To be easier, one can build a table by giving values to x and calculate de values of f(x), obtaining points to plot the graph. One point is already known,  is the (0, 0) point.

if x = 1 then, f(x) = 2