To determine the correct function from the mapping diagram you've described, we need to analyze the relationship between the values in oval x and oval y.
Since the specific values and their relationships are not provided in your description, I can't explicitly derive the function without that information. However, I can guide you on how to find the equation by using a systematic approach:
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Identify the Values: Determine the values present in oval x and oval y, and analyze how the values from x relate to those in y.
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Look for Patterns: Check if there is a consistent additive (constant) or multiplicative (coefficient) relationship between the values, typically a linear function of the form \( f(x) = mx + b \).
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Determine the Constants:
- If you notice that each value in y is the result of multiplying (scaling) the corresponding value in x and potentially adding or subtracting a constant, you can set up the equation accordingly.
- For example, if you determine through observation that y values are derived from x by multiplying by 8 and then subtracting 12, you would consider \( f(x) = 8x - 12 \).
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Check Each Option: Based on the relationships you find in the pairs, match them with the options given:
- If you derive that \( f(x) = 8x - 12 \), that would match the first option.
- If the relationship seems to involve a different transformation or scaling, refer to the other options accordingly.
If you manage to find out how the values correspond, you can choose the correct function from the options you listed. If you provide the actual values or examples from the ovals, I can help analyze them more specifically to reach the correct equation.