Graph the function. *y=*3/2*x^*3. Plot five points on the graph of the function: one point with x=0. two points with negative *x*-values, and two points with positive *x*-values. Then click on the graph-a-function button.

Here is the graph of the function \(y = \frac{3}{2}x^3\). The red points represent the specific points requested:

1. \((0, 0)\)
2. \((-2, -12)\)
3. \((-1, -1.5)\)
4. \((1, 1.5)\)
5. \((2, 12)\)

The graph shows the typical cubic curve shape, with the function passing through these points.

Would you like more details, or do you have any questions?

Here are five related questions to further your understanding:

1. How does changing the coefficient (like \(\frac{3}{2}\) in this function) affect the graph of a cubic function?
2. What are the general shapes of polynomial functions with different degrees?
3. How do you determine if a cubic function has inflection points?
4. Can a cubic function have more than one real root? If so, how can they be found?
5. How do transformations like shifting and stretching affect the graph of cubic functions?

**Tip:** When graphing functions, identifying key points (like intercepts and turning points) can help provide a clear picture of the function's behavior.

Explore how to graph the cubic function y = (3/2)x^3 with specific points plotted, including the origin, negative and positive x-values. Understand the behavior of cubic functions and their graphical representations. Suitable for high school students studying graphing and cubic functions.

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