To correctly determine the piecewise function that represents the description of the rays plotted, we need to consider the key points mentioned:
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First ray starting from an open endpoint: This typically indicates that the function is valid up to but not including a specific x-value (which might indicate a starting point for y). For instance, if it’s starting from something like (2, -2) but not including that point, the function would be written as some constant value for x less than 2 (or the equivalent for x greater than 2 if going in the opposite direction).
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Second ray starting from a closed endpoint: This means that the function includes the value at a specific x-value. For instance, at x = 3, if the line has a closed dot, the function would be defined there.
With these considerations, let’s analyze the options:
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y={−2, x>23, x≤3: There’s a potential misunderstanding with the notation; it suggests two separate pieces, but they're not coherent; it doesn’t clearly define for x values regarding how the graphs start.
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y={−2, x>03, x>0: Similar issue as before; it compares ranges without clarity on a legitimate piecewise format.
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y={−2x3x: This doesn't make sense as a piecewise function; it appears to be mixing points and specific calculations or linearity which doesn’t match the description.
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y={−2, x<03, x≥0: This also fails in notation, but if “x<0” is taken to mean values less than zero and “3” as open for less than or equal means the constants are defined properly (but it should clarify basic range determination correctly).
To summarize, without seeing the specific rays and their plotted positions, we can analyse these choices further, but based solely textually without context from an image:
Best guess might be:
- Each piece must show a distinct range of x values, with “−2” indicating a horizontal line up to some point, and then transitioning to “3” for x-values equal or greater.
Thus, the likely working piece is aligned closest to “y={−2, x<03, x≥0” for reasoning, where it overlaps indicating a continuous connection of rays; check confirmed details by visual representation.
For ultimate decision, it’s necessary to evaluate plotted coordinates/symbol clarity directly alongside listed mathematical pieces both in format and definition previously described (open/closed dots must match format definitions correctly).
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