To determine which option matches the S-shaped curve on the coordinate plane, we need to analyze the two given functions:
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Option #1: \( f(x) = \sqrt{x} - 3 \)
- This function has its graph only defined for \( x \geq 0 \) since the square root of a negative number is not defined in the set of real numbers. The graph will start at \( (-3) \) when \( x = 0 \) and will rise gradually as \( x \) increases.
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Option #2: \( f(x) = \sqrt{x} \)
- Similar to Option #1, this function is also only defined for \( x \geq 0 \). The graph starts at the origin (0,0) and rises gradually as \( x \) increases.
Now let's consider that the S-shaped curve typically signifies a function that has both positive and negative values over a range of \( x \), which neither of these options exhibit since they are limited to the non-negative domain.
Given that neither function seems to match an S-shaped curve produced in your context (such as a logistic function or certain polynomial shapes), we may need to verify which is closer to any particular plotted behavior if any of the two options are indeed represented on the graph.
However, without being able to see the specific "S-shaped" curve described in the question, I can only conclude:
If the curve starts from the left (negative) side of the graph and goes up, Option #1 would not be appropriate.
Thus, if we simply look for a potential match with the characteristics I would suggest:
- If the S-shaped curve covers values across the axes and starts in negative values, it wouldn’t match either option.
- If you had to select an option, then Option #2 \( f(x) = \sqrt{x} \) simply would match the trend of an increase from \( (0,0) \).
In summary, based on standard characteristics of the descriptions given, the relevant choice here (assuming it is only considering basic shapes and not analyzing if it matches specifically against the S-curve beyond its positive domain nature) is:
Option #2: \( f(x) = \sqrt{x} \)