Answer:
[tex]F(x)=\left \{ {{-\frac{1}{2}+1, x<0 } \atop {2x-2, x\geq0}} \right.[/tex]
Step-by-step explanation:
There are 2 linear equations, one with an open circle and one with a closed one. Depending on where the circle is, that will tell you your start. Both circles start at 0 on the graph. The open circle means that the first equation will be x < 0. The second equation has a closed circle so it will be [tex]x\geq 0[/tex] because the linear equation is increasing positively.
Now you need to the start point of both equations.
[tex]x<0[/tex] start point is 1 on the y-axis
[tex]x\geq 0[/tex] start point is 2 on the y-axis
Now you have to find the slope for the two equations
[tex]x<0[/tex] the equation goes up 1 and and over 2
[tex]x\geq 0[/tex] the equation goes up 2 and over 1
Now put together the equations
[tex]x<0[/tex] [tex]\frac{-1}{2} + 1[/tex]
[tex]x\geq 0[/tex] [tex]2x - 2[/tex]
