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The given problem asks to find the new vertices of the cubic function \( \frac{1}{3} c(x) \) when the vertices of the original cubic function \( c(x) \) are at \( (-3, 1) \) and \( (2, -9) \).

When we scale a function by a factor, such as \( \frac{1}{3} \), it only affects the *y*-coordinates of the points (since the *x*-coordinates remain unchanged). Specifically, multiplying the function by \( \frac{1}{3} \) scales the *y*-values by \( \frac{1}{3} \), but the *x*-values stay the same.

### Step-by-Step Solution:
1. The vertices of \( c(x) \) are \( (-3, 1) \) and \( (2, -9) \).
2. For \( \frac{1}{3} c(x) \), multiply the *y*-coordinates of these vertices by \( \frac{1}{3} \).

For the vertex \( (-3, 1) \):
- The new *y*-coordinate will be \( \frac{1}{3} \times 1 = \frac{1}{3} \).
- The vertex becomes \( (-3, \frac{1}{3}) \).

For the vertex \( (2, -9) \):
- The new *y*-coordinate will be \( \frac{1}{3} \times (-9) = -3 \).
- The vertex becomes \( (2, -3) \).

### Final Answer:
The new vertices of \( \frac{1}{3} c(x) \) are:
- \( (-3,\frac{1}{3}) \)
- \( (2,-3) \)

Would you like more details or have any other questions? Here are 5 related questions you might find helpful:

1. How does scaling a function affect its graph geometrically?
2. What happens to the *x*-coordinates when a function is vertically stretched or compressed?
3. What is the difference between vertical and horizontal scaling of a function?
4. How would the transformation change if the function were scaled by a negative factor?
5. How do transformations such as translations and reflections affect the vertices of a function?

**Tip:** Always remember that vertical transformations of a function affect the *y*-coordinates, while horizontal transformations affect the *x*-coordinates.

The vertices of cubic function c(x) are located at (-3,1) and (2,-9). Where are the vertices of (1/3)c(x) located? Enter your responses as ordered pairs. Do not include any spaces.

Learn how to find the new vertices of a cubic function (1/3)c(x) when the original vertices are given. This problem covers function transformations and scaling, suitable for high school students in Grades 9-12.

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