Constant function, Linear function and Affine function

Classify the following functions indicating the type and the slope:

  1. $y=-2x + 1$

  2. $y=-1$

  3. $y = x$

Let's start with the first one:

  1. $y=-2x + 1$

We observe that the expression is of the type $y= mx + n$, with

$$m =-2$$

$$n = 1$$

Therefore it is an affine function with slope $-2$.

  1. $y =-1$

In this case the function corresponds to one of the type $f(x) = k$, where $k$ is constant.

Therefore, this is a constant function with slope $0$.

  1. $y = x$

Finally, we have a function of the type $f(x) = mx$ with $m = 1$.

Therefore this is a linear function with slope $m = 1$.

  1. $y=-2x + 1$

Affine function.

Slope $m = -2$.

  1. $y =-1$

Constant function.

Slope $m = 0$.

  1. $y= x$

Linear function.

Slope $m = 1$.

Back to topic