The points (-5, 1), (-2, 4), (2, 4), and (-5, 1) gives the piecewise defined function as the second option;
g(x) = x + 6, when x < -2
g(x) = x², when -2 ≤ x < 2
g(x) = 6 - x, when x ≥ 2
<h3>How can the correct piecewise defined function be found?</h3>
Parts of the function are:
x < -2
Slope = (4-1)/(-2-(-5)) = 1
Equation is: g(x) - 4 = x - (-2)
g(x) - 4 = x + 2
g(x) = x + 2 + 4 = x + 6
In the region, -2 ≤ x < 2, points on the graph are;
(-2, 4), (0, 0), (2, 4)
The above points corresponds with the function;
In the region x ≥ 2, we have;
Slope = -1
Equation is: g(x) - 4 = -1×(x - 2) = 2 - x
Therefore;
g(x) = 4+2 - x = 6 - x
The rule for the piecewise defined function is therefore;
- g(x) = x + 6, when x < -2
- g(x) = x², when -2 ≤ x < 2
- g(x) = 6 - x, when x ≥ 2
The correct option is therefore the second option;
Learn more about piecewise defined functions here:
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