how to draw coordinates linear equation

Question

The function $f$ is defined by

$$f(x) =\begin{cases} -\frac x3 -4/3 & \ -1 \le x<2 \\ 3x -8 & 2\le x\le 5 \end{cases}$$

Now I am trying to draw $y= f(x)$

I started by mapping out the $x$ and $y$ like this

• $x=-1, y=-1$
• $x=0, y=-4/3$
• $x=1, y=-5/3$
• $x=2, y=-2$
• $x=3, y=1$
• $x=4, y=4$
• $x=5, y=7$

And all I have to do is draw the line to the points right ? I am asking because I was confused by the two conditions and Want to confirm that I am doing it right

Answer 1

The first part is defined by the segment

• left point: $\left(-1,-1\right)$
• right point: $\left(2,-2\right)$

and the second part is defined by the segment

• left point: $\left(2,-2\right)$
• right point: $\left(5,7\right)$