https://file.aiquickdraw.com/mathbot/file/172980766386547s1dpqe.jpg

The function you are asked to graph is:

\[
y = \frac{1}{2} x^3
\]

Let's go through how to plot five points, including one for \(x = 0\), two for negative \(x\)-values, and two for positive \(x\)-values.

1. **Point at \(x = 0\)**:
   \[
   y = \frac{1}{2} (0)^3 = 0
   \]
   So, the point is \((0, 0)\).

2. **Choose two negative \(x\)-values**:
   - For \(x = -2\):
     \[
     y = \frac{1}{2} (-2)^3 = \frac{1}{2} (-8) = -4
     \]
     The point is \((-2, -4)\).
   - For \(x = -1\):
     \[
     y = \frac{1}{2} (-1)^3 = \frac{1}{2} (-1) = -0.5
     \]
     The point is \((-1, -0.5)\).

3. **Choose two positive \(x\)-values**:
   - For \(x = 1\):
     \[
     y = \frac{1}{2} (1)^3 = \frac{1}{2} (1) = 0.5
     \]
     The point is \((1, 0.5)\).
   - For \(x = 2\):
     \[
     y = \frac{1}{2} (2)^3 = \frac{1}{2} (8) = 4
     \]
     The point is \((2, 4)\).

### Points to plot:
1. \((0, 0)\)
2. \((-2, -4)\)
3. \((-1, -0.5)\)
4. \((1, 0.5)\)
5. \((2, 4)\)

Would you like further details or assistance with another step? Here are some related questions:

1. How do cubic functions behave as \(x \to \infty\) or \(x \to -\infty\)?
2. What are the key differences between cubic and quadratic graphs?
3. How do changes in coefficients affect the shape of a cubic function?
4. How can we determine if a cubic function has inflection points?
5. What real-life applications can be modeled using cubic functions?

**Tip**: Cubic functions can either increase or decrease sharply depending on the coefficient of \(x^3\), creating their characteristic "S" shape.

Graph the function y = (1/2) 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.

Learn how to graph the cubic function y = (1/2) x^3 by plotting key points on the graph. This lesson involves plotting points for x = 0, negative x-values, and positive x-values. Ideal for high school students learning graph transformations of cubic functions.

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