To determine if the graph accurately displays the function \( f(x) = 4x^3 - x \), we can calculate the values of \( f(x) \) for the given inputs of \( -3, -2, -1, 0, \) and \( 1 \) and use an input-output table.
Calculating \( f(x) \):
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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 have the following input-output table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -3 & -105 \ -2 & -30 \ -1 & -3 \ 0 & 0 \ 1 & 3 \ \hline \end{array} \]
Now, if you can compare these values with the corresponding points on the graph, we can determine if the graph is accurate or not. Based on this table:
- Verify the points \((-3, -105)\), \((-2, -30)\), \((-1, -3)\), \( (0, 0) \), and \((1, 3)\) on the graph.
If all calculated points correspond to the points on the graph, then you would enter 1. If any of these points do not match the graph, then you would enter 2.
Since I cannot see the graph itself, I will instruct you to compare the values based on the calculations provided, and you can make the decision based on the comparison.