To match the descriptions with the correct function, let's analyze the given data for Function A and Function B, and then compare them to Function C.
Analysis of Function A (x, y)
- \( (0, 1) \): When \( x = 0 \), \( y = 1 \)
- \( (4, 9) \): When \( x = 4 \), \( y = 9 \)
- \( (8, 17) \): When \( x = 8 \), \( y = 17 \)
Analyzing the pattern:
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From the points:
- At \( x = 0, y = 1 \)
- At \( x = 4, y = 9 \) (Increase by 8)
- At \( x = 8, y = 17 \) (Increase by 8)
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The difference in \( y \) values is consistent and suggests a linear relationship.
Finding the function:
A simple function in the form of \( y = mx + b \) would be suitable. Let's solve for \( m \) and \( b \).
- From the two points:
- From (0,1): \( b = 1 \)
- Assuming \( y = mx + 1 \)
- Using (4,9): \( 9 = 4m + 1 \) → \( 8 = 4m \) → \( m = 2 \)
Thus, Function A appears to be represented as: \[ y = 2x + 1 \]
Now looking at Function B:
We don't have specific values, so let's assume it’s an unknown relationship.
Function C: \( y = x + 20 \)
This is a linear function where each \( x \) translates to \( y \) simply by adding 20.
Conclusions:
- Function A corresponds to \( y = 2x + 1 \).
- Function C is clearly \( y = x + 20 \).
- Function B would then imply some other function not in your data, possibly with a different linear slope than Function A.
In summary, we have:
- Function A: \( y = 2x + 1 \) (matches the given point data),
- Function C: \( y = x + 20 \) (directly given),
- Function B: assumed to be different and does not have data provided in your context.
Thus, if I were to match based only on the description provided, the matches would be:
- Function A: \( y = 2x + 1 \) (based on points),
- Function C: \( y = x + 20 \).
- Function B would not be specifically identified without additional description.
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