Information

1st degree function


Definition

It's called polynomial function of the 1st degree, or similar function, to any function f IR to IR given by a law of the form f (x) = ax + b where a and b are given real numbers and a0.

In function f (x) = ax + b, the number The is called the coefficient of x is the number B It is called constant term.

Here are some examples of 1st degree polynomial functions:

f (x) = 5x - 3, where a = 5 and b = - 3
f (x) = -2x - 7, where a = -2 and b = - 7
f (x) = 11xwhere a = 11 and b = 0

Graphic

The graph of a polynomial function of the 1st degree, y = ax + b, with a0, is an oblique line to the axes Ox it's they. For example, let's build the graph of the function y = 3x - 1:

As the graph is a straight line, just get two of its points and connect them with the help of a ruler:

a) To x = 0, we have y = 3 · 0 - 1 = -1; therefore, a point is (0, -1).
b) To y = 0, we have 0 = 3x - 1; therefore, and another point is .

We mark the points (0, -1) and in the Cartesian plane and connect the two with a straight line.

xy
0-1
0

We have already seen that the graph of the related function y = ax + b is a straight line.

The coefficient of x, The, is called angular coefficient of the line and, as we shall see, it is linked to the slope of the line with respect to the O axisx.

The constant term, B, is called the linear coefficient of the line. For x = 0, we have y = a · 0 + b = b. Thus, the linear coefficient is the ordinate of the point at which the line cuts the O axis.y.

Next: Zero or Function Root