To determine which graph accurately represents the function \( f(x) = \frac{1}{2}x + 3 \) with the inputs of -4, -2, 0, 2, and 4, we can first create an input-output table.
Let's calculate \( f(x) \) for the specified inputs:
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For \( x = -4 \): \[ f(-4) = \frac{1}{2}(-4) + 3 = -2 + 3 = 1 \]
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For \( x = -2 \): \[ f(-2) = \frac{1}{2}(-2) + 3 = -1 + 3 = 2 \]
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For \( x = 0 \): \[ f(0) = \frac{1}{2}(0) + 3 = 0 + 3 = 3 \]
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For \( x = 2 \): \[ f(2) = \frac{1}{2}(2) + 3 = 1 + 3 = 4 \]
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For \( x = 4 \): \[ f(4) = \frac{1}{2}(4) + 3 = 2 + 3 = 5 \]
Now, we can summarize the input-output table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -4 & 1 \ -2 & 2 \ 0 & 3 \ 2 & 4 \ 4 & 5 \ \hline \end{array} \]
Based on this table, the ordered pairs are:
- (-4, 1)
- (-2, 2)
- (0, 3)
- (2, 4)
- (4, 5)
You would then compare these points to the graphs provided to find the one that accurately represents the function \( f(x) = \frac{1}{2}x + 3 \). Look for a line passing through these points.
If a graph contains points (-4, 1), (-2, 2), (0, 3), (2, 4), and (4, 5), that would be the correct representation.