To determine the correct function notation for the data in the table, we need to analyze the provided data points. The table shows pairs of \(x\) and \(y\) values, but part of it seems to be missing. Let's assume the complete pairs are:
- When \(x = 0\), \(y = 3\)
- When \(x = 1\), \(y = 312\)
- When \(x = 2\), \(y = 4\)
- When \(x = 3\), \(y = 412\)
- When \(x = 4\), \(y = 1\)
Note that there seem to be inconsistencies in expected behavior (for example, \(y\) is much larger for some \(x\) values). However, to find a function that might fit a pattern, we should examine it.
Looking through the answer choices:
- \(f(x) = 3x + 12\)
- \(f(x) = 3x + \frac{1}{2}\)
- \(f(y) = 3x + 12\)
- \(f(y) = 3x + \frac{1}{2}\)
- \(f(y) = 12x + 3\)
- \(f(y) = \frac{1}{2}x + 3\)
- \(f(x) = 12x + 3\)
Unfortunately, the provided data does not lend itself clearly to a simple linear equation, nor does it clarify which pair of \(x\) and \(y\) you want to evaluate with more context.
However, let's look at the answers: Only equations \(f(x)\) would likely be acceptable, as \(f(y)\) suggests a different approach.
Assuming points dropped in are misaligned, letβs summarize likely relationships manually if:
If we found that at point (0,3), for instance, we might pick \(f(x) = 3\) (a constant), but the growth of points leads to more attention.
Testing simple relationships on \(f(x)\):
- If \(f(x) = 12x + 3\), then:
- When \(x = 0\), \(y = 3\) β
- When \(x = 1\), \(y = 12 + 3 = 15\) Γ
- In other cases, too, values may violate even more.
Ultimately, without correct patterns being followed, if based accurately only on above, \(f(x) = 12x + 3\) could fit simple starting points yielding best fitting value at the lowest inputs.
If you need a precise fit, please double-check provided pairs in full table for any entries as numerical discrepancies alter observed trendlines.