Classify the following functions indicating the type and the slope:
1) $$y=-2x + 1$$
2) $$y=-1$$
3) $$y = x$$
See development and solution
Development:
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 $$-2$$.
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 $$0$$.
3) $$y = x$$
Finally, we have a function of the type $$f(x) = mx$$ with $$m = 1$$.
Therefore this is a linear function with slope $$m = 1$$.
Solution:
1) $$y=-2x + 1$$
Affine function.
Slope $$m = -2$$.
2) $$y =-1$$
Constant function.
Slope $$m = 0$$.
3) $$y= x$$
Linear function.
Slope $$m = 1$$.