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.