Graph of a function

Consider the following function defined in parts:

$$ f(x)=\Bigg\lbrace \begin{eqnarray} x+2 & \mbox{si} & x\leq 0 \\\\ 2 & \mbox{si} & 0 < x \leq 2 \\\\ -x+4 & \mbox{si} & x>2 \end{eqnarray}$$

Do the graphic representation.

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:

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