What is an affine function?
An affine function, also known as first degree polynomial function, is a function of f : ℝ→ℝ, defined as the form y=ax+b or f(x) = ax + b, where a and b are real numbers and a ≠ 0, b ≠ 0.
In this type of functions the a is called the coefficient of x and represents the growth rate, variation rate or angular coefficient. The b is called the constant term and represents the y-interception.
What is the graph of an affine function?
The graph of an affine function is a straight line that intercepts the y-axis in the point (0, b). To plot the graph, one needs to know at least two points.
For example, to plot the graph of y = 3x + 6, first it is necessary to calculate the root (or zero) of the function. The root, or zero, is where the function intercepts the x-axis, and can be calculated equalizing y=0.
3x + 6 = 0 -> x = -2
So, one point is (0, 6) and the other point is (-2, 0).
Having two known points, one can plot the graph such as:
Affine 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.