To identify the function that models the given points \((1, 3)\), \((2, 6)\), \((3, 9)\), and \((4, 12)\), we can first look for a pattern in the \(y\) values relative to the \(x\) values.
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Identify the relationship:
- For \(x = 1\), \(y = 3\)
- For \(x = 2\), \(y = 6\)
- For \(x = 3\), \(y = 9\)
- For \(x = 4\), \(y = 12\)
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Determine the pattern: Observing the \(y\) values, we see:
- \(3 = 1 \times 3\)
- \(6 = 2 \times 3\)
- \(9 = 3 \times 3\)
- \(12 = 4 \times 3\)
It appears that the \(y\) values are equal to \(3\) times the \(x\) values.
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Function representation: The function that describes this relationship can be written as: \[ y = 3x \]
Thus, the function modeled by the pattern is \(y = 3x\).