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.