To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the given inputs of \( -4, -2, 0, 2, \) and \( 4 \), we first need to calculate the outputs (or \( y \)-values) for each of these inputs.
Let's compute the function 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 input-output pairs: \[ \begin{align*} (-4, -45) \ (-2, -21) \ (0, 3) \ (2, 27) \ (4, 51) \ \end{align*} \]
Next, let's analyze the potential graphs. The function is a linear equation, and based on the calculated outputs, we expect the coordinates to fall within a certain range on the y-axis. Here are the outputs we expect based on our calculations:
- The \( y \)-values range roughly from \(-45\) to \(51\).
Given the provided descriptions of the graphs, we can conclude:
- The graph plotted within the ranges from \(-10\) to \(10\) cannot accurately display any of our outputs, as our maximum output is \(51\) and our minimum output is \(-45\).
- The other graph that ranges from \(0\) to \(7\) is also not appropriate, as our output values are not within that range.
However, none of the provided graphs have the appropriate scaling to represent the outputs accurately. Based on the calculations, all feasible values lie far outside the ranges of the y-axes indicated in the graph descriptions.
As such, if you are forced to select based on appearances, look for any graphs that might scale at a higher value (if there were any additional options outside this or an error in the y-values' scaling), but based strictly on the outputs calculated, none of the offered descriptions match the appropriate function graph for \( f(x) = 12x + 3 \).
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