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To evaluate \( f(-7.6) \) for the function \( f(x) = 13x^3 + 4x^2 - 15.5x - 11 \), we substitute \( x = -7.6 \) and compute each term.

### Steps
1. Substitute \( x = -7.6 \) into the function:
   \[
   f(-7.6) = 13(-7.6)^3 + 4(-7.6)^2 - 15.5(-7.6) - 11
   \]

2. Calculate each term individually:
   - **First term:** \( 13 \times (-7.6)^3 \)
   - **Second term:** \( 4 \times (-7.6)^2 \)
   - **Third term:** \( -15.5 \times (-7.6) \)
   - **Constant term:** \(-11\)

3. Add the results of these calculations and round to two decimal places.

Let’s go through each of these calculations:

- **First term:** 
  \[
  13 \times (-7.6)^3 = 13 \times (-438.976) = -5706.688
  \]

- **Second term:** 
  \[
  4 \times (-7.6)^2 = 4 \times 57.76 = 231.04
  \]

- **Third term:** 
  \[
  -15.5 \times (-7.6) = 117.8
  \]

- **Constant term:** \(-11\)

4. Now, add these terms together:
   \[
   f(-7.6) = -5706.688 + 231.04 + 117.8 - 11 = -5368.848
   \]

5. Rounding to two decimal places, we get:
   \[
   f(-7.6) \approx -5368.85
   \]

### Final Answer
\[
f(-7.6) = -5368.85
\]

Would you like a breakdown of any specific step? 

Here are some related questions to deepen your understanding:
1. How do you evaluate functions at other values of \( x \)?
2. What is the importance of rounding in real-world applications?
3. How does changing the coefficients affect the function?
4. What role does each term play in shaping the graph of a polynomial function?
5. How do we interpret negative values in polynomial function results?

**Tip:** Always follow the order of operations (PEMDAS) when evaluating functions.

Evaluate f(-7.6), where f(x) = 13x^3 + 4x^2 - 15.5x - 11. Your solution should be given correct to two decimal places.

Learn how to evaluate the function f(x) = 13x^3 + 4x^2 - 15.5x - 11 at x = -7.6 with detailed step-by-step calculations. This example covers polynomial function evaluation and is suitable for students in Grades 10-12.

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