To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the inputs \(-4, -2, 0, 2, 4\), we first need to calculate the output for each input using the function.
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For \( x = -4 \): \[ f(-4) = 12(-4) + 3 = -48 + 3 = -45 \]
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For \( x = -2 \): \[ f(-2) = 12(-2) + 3 = -24 + 3 = -21 \]
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For \( x = 0 \): \[ f(0) = 12(0) + 3 = 0 + 3 = 3 \]
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For \( x = 2 \): \[ f(2) = 12(2) + 3 = 24 + 3 = 27 \]
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For \( x = 4 \): \[ f(4) = 12(4) + 3 = 48 + 3 = 51 \]
Now we have the following input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Next, we need to examine the provided options and check if a graph corresponds to these points.
Looking at the outputs calculated:
- The x-values range between \(-4\) and \(4\).
- The y-values range from \(-45\) to \(51\), which is a very wide range, suggesting that the y-axis will need to have significant values for both ranges.
Among the options you provided, the one with the x-axis ranging from \(-4\) to \(4\) and the y-axis from approximately \(-50\) to \(60\) would be a valid candidate to capture all points accurately, especially since most others seem limited.
Unfortunately, since I cannot see the graphs directly, I recommend selecting the graph with the x-axis ranging from \(-4\) to \(4\) and a sufficient y-axis range to include the output values computed above. This is more likely to correctly represent the function \( f(x) = 12x + 3 \) with the specified inputs.
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