To evaluate whether the graph accurately represents the piecewise function given, we should analyze the endpoints of the defined intervals and how they relate to the function.
The piecewise function is defined as follows:
- \( f(x) = 0.5 \) if \( 1 \leq x \leq 3 \)
- \( f(x) = 1.0 \) if \( 3 < x \leq 6 \)
- \( f(x) = 0.5x \) if \( x > 6 \)
Now, let's consider the continuity and the endpoints of each piece:
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For \( f(x) = 0.5 \) in the interval \( [1, 3] \), the endpoints at \( x=1 \) and \( x=3 \) should both be closed circles because it's inclusive (both 1 and 3 are part of this interval).
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For \( f(x) = 1.0 \) in the interval \( (3, 6] \), at \( x=3 \) there should be an open circle (indicating that 3 is not included), and at \( x=6 \) there should be a closed circle (since 6 is included in that piece).
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For \( f(x) = 0.5x \) in the interval \( (6, \infty) \), at \( x=6 \) there should be an open circle (indicating that 6 is not included), since this part starts right after 6.
With this analysis, we can conclude:
- There should be an open circle at \( x=3 \) and \( x=6 \) to indicate that those points are not included in the second and third piece of the function, respectively.
Since the function does have open circles at those points, the correct response would be:
No. There should be an open circle on the first point of two parts of the function.
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