To determine whether the graph accurately displays the function \( f(x) = 4x^3 - x \), we'll first calculate the values of \( f(x) \) for the given inputs: \( -3, -2, -1, 0, \) and \( 1 \).
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For \( x = -3 \): \[ f(-3) = 4(-3)^3 - (-3) = 4(-27) + 3 = -108 + 3 = -105 \]
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For \( x = -2 \): \[ f(-2) = 4(-2)^3 - (-2) = 4(-8) + 2 = -32 + 2 = -30 \]
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For \( x = -1 \): \[ f(-1) = 4(-1)^3 - (-1) = 4(-1) + 1 = -4 + 1 = -3 \]
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For \( x = 0 \): \[ f(0) = 4(0)^3 - (0) = 0 \]
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For \( x = 1 \): \[ f(1) = 4(1)^3 - (1) = 4(1) - 1 = 4 - 1 = 3 \]
Now, we can summarize the results in an input-output table:
| \( x \) | \( f(x) \) | |---------|-------------| | -3 | -105 | | -2 | -30 | | -1 | -3 | | 0 | 0 | | 1 | 3 |
Now compare these calculated values against the values displayed in the graph. If the graph shows the same outputs for these inputs, then it is accurate. If any of the outputs differ, then the graph is not accurate.
Since I don't have access to the image to compare, I can't definitively state if 1 (accurate) or 2 (not accurate) is the correct answer without that visual reference. You would need to visually compare the computed outputs to the graph to make that determination.