To plot the function \( y = -\frac{13}{8}x^3 \), let's first find the corresponding \( y \)-values for the specified \( x \)-values:
Points with Calculated \( y \)-Values:
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For \( x = 0 \): \[ y = -\frac{13}{8}(0)^3 = 0 \implies (0, 0) \]
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For \( x = -1 \): \[ y = -\frac{13}{8}(-1)^3 = -\frac{13}{8}(-1) = \frac{13}{8} \implies (-1, \frac{13}{8}) \approx (-1, 1.625) \]
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For \( x = -2 \): \[ y = -\frac{13}{8}(-2)^3 = -\frac{13}{8}(-8) = \frac{104}{8} = 13 \implies (-2, 13) \]
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For \( x = 1 \): \[ y = -\frac{13}{8}(1)^3 = -\frac{13}{8} \implies (1, -\frac{13}{8}) \approx (1, -1.625) \]
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For \( x = 2 \): \[ y = -\frac{13}{8}(2)^3 = -\frac{13}{8}(8) = -13 \implies (2, -13) \]
Summary of Points:
- \( (0, 0) \)
- \( (-1, \frac{13}{8}) \) or approximately \( (-1, 1.625) \)
- \( (-2, 13) \)
- \( (1, -\frac{13}{8}) \) or approximately \( (1, -1.625) \)
- \( (2, -13) \)
Visual Representation:
You can now plot these points on a coordinate system:
- (0, 0)
- (-1, 1.625)
- (-2, 13)
- (1, -1.625)
- (2, -13)
After plotting these points, you can use the graphing tool to visualize the overall graph of the function \( y = -\frac{13}{8}x^3 \).
If you're using a graphing calculator or software, input the function and see how it creates the curve that connects these five points. The graph will show the characteristic "S" shape of a cubic function, where it decreases for positive \( x \) and increases for negative \( x \).