To create an input-output table for the function \( f(x) = \frac{1}{2}x + 3 \), we will calculate the output \( f(x) \) for each input \( x \) given in the problem: -4, -3, 0, 2, and 4.
Here are the calculations:
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For \( x = -4 \): \[ f(-4) = \frac{1}{2}(-4) + 3 = -2 + 3 = 1 \]
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For \( x = -3 \): \[ f(-3) = \frac{1}{2}(-3) + 3 = -1.5 + 3 = 1.5 \]
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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 compile these results into an input-output table:
| \( x \) | \( f(x) \) | |---------|------------| | -4 | 1 | | -3 | 1.5 | | 0 | 3 | | 2 | 4 | | 4 | 5 |
Summary of Results:
- \( f(-4) = 1 \)
- \( f(-3) = 1.5 \)
- \( f(0) = 3 \)
- \( f(2) = 4 \)
- \( f(4) = 5 \)
With this table, you can now visually compare the corresponding values to the graphs available to find the one that accurately represents the function \( f(x) = \frac{1}{2}x + 3 \). Look for a graph that passes through the points:
- (-4, 1)
- (-3, 1.5)
- (0, 3)
- (2, 4)
- (4, 5)
The correct graph will consistently show these values.