We have a piecewise function.
Therefore, to find the function, we must evaluate each domain separately.
We have then:
For [tex]x \leq -2[/tex]:
The function for this domain is:
[tex] y = -3
[/tex]
For [tex]-2 \ \textless \ x \leq 2[/tex]:
The function for this domain is:
[tex] y = mx + b
[/tex]
Where,
[tex] b = -3
m = (y2 - y1) / (x2 - x1)
m = (1 - (-7)) / (2 - (-2))[/tex]
[tex] m = (1 + 7) / (2 + 2)
m = 8/4
m = 2[/tex]
Substituting:
[tex] y = 2x - 3
[/tex]
For [tex]x\ \textgreater \ 2[/tex]:
The function for this domain is:
[tex] y = 5[/tex]