9514 1404 393
Answer:
[tex]y=\left\{ \begin{array}{rc} {-x+3, &\text{for $x<-2$}} \\ {-2, &\text{for $x=-2$}} \\ {x+4, &\text{for $x>-2$}}}\end{array} \right.[/tex]
Step-by-step explanation:
The line to the upper left has a slope of -1. If it were extended, it would intersect the y-axis at y=3, so its equation is ...
y = -x +3
The line to the upper right has a slope of +1 and a y-intercept of 4, so its equation is ...
y = x + 4
At x=-2, the function is defined as -2.
So, the piecewise definition is ...
[tex]y=\left\{ \begin{array}{rc} {-x+3, &\text{for $x<-2$}} \\ {-2, &\text{for $x=-2$}} \\ {x+4, &\text{for $x>-2$}}}\end{array} \right.[/tex]
