To determine which graph accurately represents the function \( f(x) = 12x + 3 \) for the inputs \( -4, -2, 0, 2, \) and \( 4 \), we first need to calculate the corresponding \( f(x) \) values for each input:
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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 a set of points:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Next, we need to consider the characteristics of the graph based on these points:
- The x-values range from \( -4 \) to \( 4 \).
- The y-values, calculated, are quite high (especially for \( x = 2 \) and \( x = 4 \)), indicating that the graph extends significantly in the positive y-direction.
Given these points, you would look for a graph that includes:
- x-axis ranging at least from \( -4 \) to \( 4 \).
- y-axis capable of showing values down to \(-45\) and up to \(51\).
From the descriptions provided, the first and fourth response both describe graphs with suitable x-axes. However, the key to resolving the suitable graph lies in the y-range. The graph must cover from approximately \( -45 \) to \( 51\).
If all graphs indeed represent a similar interval range but the y-range is not accurately mentioned, you could determine the correctness based purely on their x-axes (since ranges vary).
You will need to double-check which graph's y-axis reaches the necessary points to make a definitive choice. Based on the calculations, the graph must include points through which the calculated output points can also be correctly plotted particularly highlighting the significant y-values.
Please reference these calculated points with the graphical representations to confirm which one meets all criteria.