Constant function, Linear function and Affine function
Classify the following functions indicating the type and the slope:
$y=-2x + 1$
$y=-1$
$y = x$
Let's start with the first one:
- $y=-2x + 1$
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 $-2$.
- $y =-1$
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 $0$.
- $y = x$
Finally, we have a function of the type $f(x) = mx$ with $m = 1$.
Therefore this is a linear function with slope $m = 1$.
- $y=-2x + 1$
Affine function.
Slope $m = -2$.
- $y =-1$
Constant function.
Slope $m = 0$.
- $y= x$
Linear function.
Slope $m = 1$.