To determine which graph correctly represents the geometric sequence given by the points \( (n, f(n)) \):
- \( n = 0, f(n) = 11 \)
- \( n = 1, f(n) = 16.5 \)
- \( n = 2, f(n) = 24.75 \)
- \( n = 3, f(n) = 37.125 \)
- \( n = 4, f(n) = 55.6875 \)
We can note that the function \( f(n) \) appears to represent a geometric progression. To verify this, we can check the ratio of successive terms:
- \( \frac{16.5}{11} = 1.5 \)
- \( \frac{24.75}{16.5} = 1.5 \)
- \( \frac{37.125}{24.75} = 1.5 \)
- \( \frac{55.6875}{37.125} = 1.5 \)
The common ratio is \( r = 1.5 \).
Now, let's consider the range of the values and the axis scaling.
- The values of \( f(n) \) range from \( 11 \) to \( 55.6875 \).
- The values on the y-axis need to include at a minimum up to \( 60 \).
When looking at the provided graph options:
- Option one: The y-axis goes from 0 to 60 (good range).
- Option two: The y-axis goes from 0 to 60 (good range).
- Option three: The y-axis goes from 0 to 6000 (too large).
- Option four: The x and y-axes are reversed, and the ranges are incorrect.
Considering the given functions and the possible ranges, options one and two both seem plausible. However, we also need to see how those points actually map.
Both option one and option two have the correct range and maintain the coordinates correctly in the first quadrant.
To conclude, both option one and option two can be correct provided that the plotted coordinates match the \( f(n) \) values accurately. As we were checking specifically, if coordination doesn't provide visual clarity or there's a misgraphing, one may be preferred over the other upon visualization.
If forced to choose without the actual images, I suggest going with option two, as it allows for a larger viewing range on the x-axis (to match the number of points plotted). However, either could suffice based on the details you have.
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