The definition of the piece-wise function is:
- [tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]
- [tex]f(x) = -3, 2 < x < 6[/tex].
What is a piece-wise function?
A piece-wise function is a function that has different definitions, depending on the input.
In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:
m = (6 - (-4))/(2 - (-2)) = 2.5.
The y-intercept is of b = 1, hence the rule is:
[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]
For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:
[tex]f(x) = -3, 2 < x < 6[/tex].
More can be learned about piece-wise functions at https://brainly.com/question/27262465
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