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The input-output table for the function \( y = 3^x \) can be completed by plugging in the values of \( x \) into the function \( y = 3^x \). Let's go through this step by step:

1. **Given Values**:
   - When \( x = -2 \), \( y = 1/9 \).
   - When \( x = -1 \), \( y = 1/3 \).
   - When \( x = 0 \), \( y = 1 \).
   - When \( x = 1 \), \( y = 3 \).
   - When \( x = 2 \), \( y = 9 \).

2. **Values to Compute**:
   - For \( x = 3 \), we need to find \( a \).
     \[
     y = 3^3 = 27
     \]
     So, \( a = 27 \).

   - For \( x = 4 \), we need to find \( b \).
     \[
     y = 3^4 = 81
     \]
     So, \( b = 81 \).

### Final Answer:
- \( a = 27 \)
- \( b = 81 \)

Would you like a detailed explanation of any specific step? Here are some questions to help expand on this concept:

1. What is the general behavior of exponential functions like \( y = 3^x \)?
2. How does the value of \( y \) change as \( x \) becomes negative?
3. Can you derive the inverse of the function \( y = 3^x \)?
4. How do transformations (e.g., shifts or stretches) affect exponential functions like \( y = 3^x \)?
5. What are the key differences between exponential growth and linear growth?

### Tip:
Remember that exponential functions grow much faster than linear or polynomial functions as \( x \) increases. This makes them important in modeling rapid growth situations like population growth or compound interest.

Complete the input-output table for the function y = 3^x. Fill in the values for a and b.

Learn how to complete the input-output table for the exponential function y = 3^x by calculating values for x = 3 and x = 4. This exercise covers exponential growth concepts and powers of 3, suitable for students in Grades 7-9.

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