To plot the points for the function \( Y = -\frac{7}{8}x^3 \), we will calculate the values of \( Y \) for various values of \( x \).
Choose x-values:
- \( x = 0 \)
- \( x = -2 \)
- \( x = -1 \)
- \( x = 1 \)
- \( x = 2 \)
Calculate corresponding y-values:
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For \( x = 0 \): \[ Y = -\frac{7}{8}(0)^3 = 0 \] → Point: \( (0, 0) \)
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For \( x = -2 \): \[ Y = -\frac{7}{8}(-2)^3 = -\frac{7}{8}(-8) = 7 \] → Point: \( (-2, 7) \)
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For \( x = -1 \): \[ Y = -\frac{7}{8}(-1)^3 = -\frac{7}{8}(-1) = \frac{7}{8} \] → Point: \( (-1, \frac{7}{8}) \)
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For \( x = 1 \): \[ Y = -\frac{7}{8}(1)^3 = -\frac{7}{8}(-1) = -\frac{7}{8} \] → Point: \( (1, -\frac{7}{8}) \)
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For \( x = 2 \): \[ Y = -\frac{7}{8}(2)^3 = -\frac{7}{8}(8) = -7 \] → Point: \( (2, -7) \)
Summary of Points:
- \( (0, 0) \)
- \( (-2, 7) \)
- \( (-1, \frac{7}{8}) \)
- \( (1, -\frac{7}{8}) \)
- \( (2, -7) \)
Plotting the Points:
Now you can use these points to graph the function. When plotting, you'll see that the function has a cubic shape and trends downward as \( x \) becomes positive. If you were to graph this, it would show a smooth curve that passes through all the mentioned points.
Graph-a-Function:
You can now plot these points and connect them to visualize the cubic function \( Y = -\frac{7}{8}x^3 \). This illustrates the function's behavior for both negative and positive values of \( x \).