To identify the value of \( k \) given the ordered pairs from a function transformation, it's important to know what type of transformation has occurred. The original ordered pair is \( (8, 2) \) and the transformed pair is \( (2, 2) \).
From this information, we can interpret that the first component of the ordered pair has undergone a transformation while the second component remains unchanged.
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No change in the second component: The value 2 remains constant in both pairs, indicating that the transformation has affected only the x-coordinate.
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Change in the first component: The transformation seems to have moved the x-coordinate from 8 to 2.
To understand this transformation mathematically, it looks like we are making a simple transformation of the form \( x = k \cdot x_0 \) where \( x_0 \) is the original x-coordinate, and \( k \) is the scaling factor.
Setting this up using the information given: \[ 2 = k \cdot 8 \]
To find \( k \): \[ k = \frac{2}{8} = \frac{1}{4} \]
Thus, the value of \( k \) is \( \frac{1}{4} \).
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