To determine the correct piecewise function, we need to analyze the given conditions of the lines on the coordinate plane.
We have two segments defined by their behaviors in different intervals:
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For the interval \(-3 \leq x < -1\): The line is constant, which indicates that the function value is a fixed number. Given the choices, this could be \(f(x) = 1\).
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For the interval \(-1 \leq x \leq 1\): The line appears to follow a linear equation. The options suggest that this could be \(f(x) = 2x - 1\).
Now, we compile these insights into a piecewise function:
The correct option which represents the graph based on the analysis is: \[ f(x) = \begin{cases} 1 & \text{for } -3 \leq x < -1 \ 2x - 1 & \text{for } -1 \leq x \leq 1 \end{cases} \]
So, the correct response from the provided choices is: f(x)={1,2x−1,−3≤x<−1−1≤x≤1.