To plot points on the graph of the function \( y = \frac{5}{4}x^3 \), we will calculate \( y \) values for the specified \( x \) values.
Points with calculated coordinates
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For \( x = 0 \): \[ y = \frac{5}{4} \cdot 0^3 = 0 \] Point: \( (0, 0) \)
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For \( x = -2 \): \[ y = \frac{5}{4} \cdot (-2)^3 = \frac{5}{4} \cdot (-8) = -10 \] Point: \( (-2, -10) \)
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For \( x = -1 \): \[ y = \frac{5}{4} \cdot (-1)^3 = \frac{5}{4} \cdot (-1) = -\frac{5}{4} = -1.25 \] Point: \( (-1, -1.25) \)
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For \( x = 1 \): \[ y = \frac{5}{4} \cdot 1^3 = \frac{5}{4} \cdot 1 = \frac{5}{4} = 1.25 \] Point: \( (1, 1.25) \)
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For \( x = 2 \): \[ y = \frac{5}{4} \cdot 2^3 = \frac{5}{4} \cdot 8 = 10 \] Point: \( (2, 10) \)
Summary of Points
Here are the five points we've calculated:
- \( (0, 0) \)
- \( (-2, -10) \)
- \( (-1, -1.25) \)
- \( (1, 1.25) \)
- \( (2, 10) \)
Now, you can plot these points on a graph and then click on the "graph-a-function" button. The graph will show a cubic function, which takes the shape of an "S" tilted to the right. The function increases for positive values of \( x \) and decreases for negative values, demonstrating the nature of cubic polynomials.