To find which graph accurately represents the function \( f(x) = 12x + 3 \) with the given inputs of \( -4, -2, 0, 2, \) and \( 4 \), we first calculate the corresponding outputs 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 can summarize the coordinate pairs \((x, f(x))\):
- For \( x = -4 \), \( f(x) = -45 \) → Coordinate: \((-4, -45)\)
- For \( x = -2 \), \( f(x) = -21 \) → Coordinate: \((-2, -21)\)
- For \( x = 0 \), \( f(x) = 3 \) → Coordinate: \((0, 3)\)
- For \( x = 2 \), \( f(x) = 27 \) → Coordinate: \((2, 27)\)
- For \( x = 4 \), \( f(x) = 51 \) → Coordinate: \((4, 51)\)
Given these values, we need to identify the graph that corresponds to this function. The graph must:
- Include the points calculated above.
- Be on an appropriate scale for both x and y values.
The outputs range significantly from \(-45\) to \(51\) for the corresponding \(x\) inputs. Therefore, it's critical to have a y-axis that can encompass these outputs when plotted against the x-axis ranging from \(-4\) to \(4\).
From the responses provided, the second graph is the only suitable option:
- It has an x-axis ranging from \(-4\) to \(4\), which encompasses our inputs.
- Its y-axis ranges from \(-10\) to \(10\), which is not sufficient since our outputs extend far beyond this range.
Since there's some ambiguity in the options, if asked to choose based solely on containment of points and appropriate axis scaling, a graph that captures output results beyond \(10\) on the y-axis should be the correct one, which currently isn't present in the listed choices. If all given graphs only have the second graph but within a limited range, that would be the closest option despite the limitation.
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