To determine whether the graph accurately represents the piecewise function given, we need to analyze the function and the graphical representation of it.
-
For the first segment \( f(x) = 0.5 \) when \( 1 \leq x \leq 3 \): This should be represented as a horizontal line segment from \( (1, 0.5) \) to \( (3, 0.5) \), with closed circles on both ends, indicating that the dosage is included at both points.
-
For the second segment \( f(x) = 1.0 \) when \( 3 < x \leq 6 \): This represents a horizontal line segment starting just after \( x = 3 \) and going to \( x = 6 \). There should be an open circle at \( (3, 1.0) \) to signify that the function does not include this point and a closed circle at \( (6, 1.0) \) since it includes \( x = 6 \).
-
For the third segment \( f(x) = 0.5x \) when \( x > 6 \): This segment is a line that starts at \( x = 6 \) and continues upwards beyond that point. Hence, there should be an open circle at \( (6, 3.0) \) (since \( f(6) = 3.0 \) and it is not included in this segment) and it continues to increase.
In summary, without the ability to see the graph, the key points are:
- Closed circles at \( x = 1 \) and \( x = 3 \) (for the first segment),
- An open circle at \( x = 3 \) (for the transition from the first to second segment),
- A closed circle at \( x = 6 \) (for the second segment),
- An open circle at \( (6, 3.0) \) where the third segment begins.
Thus, if the graph contains all three segments correctly as described and has the correct open and closed circles, then it represents the function accurately. However, if it has open circles or is continuous where it shouldn't be, for instance between the first and second segments or at the start of the third segment, then it does not accurately represent the function.
Given this analysis, the most appropriate response would be:
No. There should be an open circle on the first point of two parts of the function.