Problems from Graph of a function

Consider the following function defined in parts:

$f (x) = {\begin{array}{rcl} x + 2 & si & x \leq 0 \\ 2 & si & 0 < x \leq 2 \\ - x + 4 & si & x > 2 \end{array}$

Do the graphic representation.

See development and solution

We may realize that:

In the interval $(- \infty, 0]$ we have a straight line of slope $m = 1$ and that cuts the axis $x$ in $x = - 2$ .
In the interval $(0, 2]$ , we have a constant function $y = 2$ .
In the interval $(2, + \infty)$ we have a straight line of slope $m = - 1$ and that cuts the axis $x$ in $x = 4$ .

Therefore the graph of the function is:

imagen

imagen

Hide solution and development