To determine whether the graph accurately represents the given piecewise function, we need to evaluate the function's defined intervals and how they translate to the graph:
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For the interval \(1 \leq x \leq 3\), the function is \(f(x) = 0.5\). This means that for any \(x\) in this range, the function should display \(0.5\) as a horizontal line from \(x=1\) to \(x=3\), inclusive.
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For the interval \(3 < x \leq 6\), the function is \(f(x) = 1.0\). Thus, there should be a horizontal line at \(f(x) = 1.0\) starting just after \(x=3\) and going up to \(x=6\), inclusive.
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For the interval \(x > 6\), the function is \(f(x) = 0.5x\). This part of the function introduces a line with a slope of \(0.5\), starting from just after \(x=6\).
Now, evaluating the graph:
- Are all three segments visible?
- Are the endpoints at \(x = 3\) and \(x = 6\) correctly represented as solid or open circles, based on inclusivity?
Given the conditions of the piecewise function, the correct assessment will relate to whether the graph reflects these points—whether it has the correct open or closed circles at transition points—and whether it has discontinuities where there should be connections.
From your options, the best response can be found by ensuring:
- Yes, all points are closed where they need to be based on inclusivity.
- No, the graph should have open circles at the transitioning points between distinct pieces.
Therefore, without visual confirmation and based solely on the options provided, the most accurate response is:
No. There should be an open circle on the first point of two parts of the function. This reflects the need for the graph to appropriately represent the transition from one piece of the function to another, emphasizing discontinuity at the defined boundaries.
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