Chapter 6 Elementary Functions

Section 6.2 Linear Functions and Polynomials

6.2.4 Linear Affine Functions

Combining linear functions with constant functions results in so-called linear affine functions. These are the sum of a linear function and a constant function. Generally, without any specification for the slope ( m) this is written as follows:

f:  { xmx+c.

The graphs of linear affine functions are also called lines. For linear affine functions, the constant m is still called slope, and the constant c is called y-intercept. The reason for this term is as follows: if the intersection point of the graph of the linear affine function with the vertical axis is considered, then this point has the distance c from the origin (see figure above). So, for the linear affine function shown in the figure below

f:  { x-2x-1

we have the slope m=-2 and the y-intercept c=-1. The y-intercept is the value of the function at x=0 and hence given by


Exercise 6.2.4
Find the slope and the y-intercept of the function

f:  { xπx-42.

Exercise 6.2.5
Which functions are the linear affine functions that have slope m=0, and which are the ones with y-intercept c=0?