The piece-wise function shown in the graph is defined as follows:
What is a piecewise function?
A piecewise function is a function that has different definitions, depending on the input.
For x equal or less than -3, the function is constant at g(x) = 6, hence the first definition is given by:
g(x) = 6, x ≤ -3.
For x between -3 and -2, with open intervals, the function is linear with a slope of -3, hence:
g(x) = -3x + b, -3 < x < -2.
There is an open interval at (-2,6), hence we use it to find b, as follows:
6 = -3(-2) + b
b = 0.
Hence:
g(x) = -3x, -3 < x < -2.
For x of at least -2, we have a linear function with slope and intercept of 1, hence:
g(x) = x + 1, x ≥ -2.
More can be learned about piece-wise functions at https://brainly.com/question/27262465
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