Since May 2021
Instructor since May 2021
Definition:
A function F defined on the reals is an affine function if and only if it is written in the following form:
F (x) = ax + b, with a and b being reals.
Example:
F (x) = 5x + 8
F (x) = x (here we have: a = 1 and b = 0, or F (x) = 1x + 0)
F (x) = -7x - 5
Counter-example :
F (x) = 2x2 + 6
F (x) = (8 / x) - 5
The form F (x) = ax + b, is not respected
Graphical representation of an affine function:
In a coordinate system, the representation of an affine function is a straight line.
Function variation:
The function has a directing coefficient, it is a. This directing coefficient manages the variation of the line, in fact:
- When a is positive, the line is strictly increasing (it goes up).
- When a is negative, the line is strictly decreasing (it goes down)?
- When a is equal to 0, the line is parallel to the x-axis.
b is the y-intercept of the line. That is to say that the line intersects the y-axis at the point of coordinates (0; b).
A function F defined on the reals is an affine function if and only if it is written in the following form:
F (x) = ax + b, with a and b being reals.
Example:
F (x) = 5x + 8
F (x) = x (here we have: a = 1 and b = 0, or F (x) = 1x + 0)
F (x) = -7x - 5
Counter-example :
F (x) = 2x2 + 6
F (x) = (8 / x) - 5
The form F (x) = ax + b, is not respected
Graphical representation of an affine function:
In a coordinate system, the representation of an affine function is a straight line.
Function variation:
The function has a directing coefficient, it is a. This directing coefficient manages the variation of the line, in fact:
- When a is positive, the line is strictly increasing (it goes up).
- When a is negative, the line is strictly decreasing (it goes down)?
- When a is equal to 0, the line is parallel to the x-axis.
b is the y-intercept of the line. That is to say that the line intersects the y-axis at the point of coordinates (0; b).
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