Bot GPT 4-o mini To determine which function corresponds to the given input-output table, we can evaluate each function at the provided values of \( x \) and compare the results with \( f(x) \) in the table.
Let's evaluate each function with the given \( x \) values:
Function 1: \( f(x) = 3x + 1 \)
- For \( x = -2 \): \[ f(-2) = 3(-2) + 1 = -6 + 1 = -5 \quad \text{(not } -11\text{)} \]
Function 2: \( f(x) = -3x^2 + 1 \)
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For \( x = -2 \): \[ f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \quad \text{(matches)} \]
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For \( x = -1 \): \[ f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \quad \text{(matches)} \]
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For \( x = 0 \): \[ f(0) = -3(0)^2 + 1 = -3(0) + 1 = 0 + 1 = 1 \quad \text{(matches)} \]
Function 3: \( f(x) = 3x^2 + 1 \)
- For \( x = -2 \): \[ f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \quad \text{(not } -11\text{)} \]
Function 4: \( f(x) = 6x + 1 \)
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For \( x = -2 \): \[ f(-2) = 6(-2) + 1 = -12 + 1 = -11 \quad \text{(matches)} \]
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For \( x = -1 \): \[ f(-1) = 6(-1) + 1 = -6 + 1 = -5 \quad \text{(not } -2\text{)} \]
Based on the evaluations above, only the function \( f(x) = -3x^2 + 1 \) matches all output values in the given table:
- For \( x = -2 \): \( f(-2) = -11 \)
- For \( x = -1 \): \( f(-1) = -2 \)
- For \( x = 0 \): \( f(0) = 1 \)
Thus, the correct function is:
f(x) = -3x² + 1
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