The piecewise functions that are represented by the graph are; g(x) = −2, x < −2; g(x) = −2x + 6, x ≥ 1; g(x) = x/2 + 1, –2 ≤ x < 1
From the attached graph of the piecewise function, we can access each option as follows;
A) g(x) = −2x, −2 < x < 0
This is not represented by the graph because g(x) = −2x has negative slope which means it goes downward. There's also no y-intercept in g(x) = −2x.
B) g(x) = −2, x < −2;
This is represented by the graph because g(x) = −2 is a horizontal line which is only on the left side of x = -2.
C) g(x) = x − 2, −2 < x < 1;
This is not represented by the graph because g(x) = x − 2 has y-intercept at y = -2 and slope of 1 which means that graph of g(x)= x - 2 must be going upward and crossing at y = -2.
D) g(x) = −2x + 6, x ≥ 1
This is represented by the graph because g(x) = −2x+6 satisfies the graph which is going downward.
E) g(x) = x/2 + 1, –2 ≤ x < 1
This is represented by the graph because g(x) = (x/2) + 1 satisfies the graph which is going downward.
The options are;
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = x/2+ 1, –2 ≤ x < 1
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