To determine whether the graph accurately displays the function \( f(x) = 4x^3 - x \), we should calculate the output values for the given input values: \( -3, -2, -1, 0, \) and \( 1 \). Then we can compare these values with the graph to see if they match.
Let's compute the function's values:
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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 computed points:
- \( f(-3) = -105 \)
- \( f(-2) = -30 \)
- \( f(-1) = -3 \)
- \( f(0) = 0 \)
- \( f(1) = 3 \)
Next, compare these outputs with the values plotted on the graph at these x-values. If all calculated function values correspond to points on the graph:
- If they match, then the graph is accurate (enter 1).
- If any do not match, the graph is not accurate (enter 2).
Since I cannot see the graph itself, I recommend you compare the computed values against the graph. Based on your comparison, enter 1 if they match or 2 if they do not match.