To determine which table of values represents an exponential function, we need to check if the $y$-values follow an exponential pattern as $x$ changes. In an exponential function, the $y$-values should change by a consistent ratio as $x$ increments.

Let's analyze each table:

1. Table 1:

   • $x$ values: -5, -2, 0, 2, 6
   • $y$ values: 26, 5, 1, 5, 37
   • This does not show a consistent multiplication ratio, so it's unlikely to be exponential.

2. Table 2:

   • $x$ values: -3, -1, 1, 3, 5, 6
   • $y$ values: -27, -1, 27, 125, 216
   • This table does not demonstrate a consistent ratio between $y$-values, so it is not exponential.

3. Table 3:

   • $x$ values: -4, -2, 0, 2, 3
   • $y$ values: 16, 4, 1, 0.25, 0.125
   • Here, the $y$-values are divided by 4 each time the $x$ values increase by 2, indicating a consistent ratio. This pattern suggests an exponential function.

4. Table 4:

   • $x$ values: 0, 4, 16, 25, 64
   • $y$ values: 0, 2, 4, 5, 8
   • This table does not demonstrate a consistent ratio and thus is not exponential.

The correct answer is Table 3 because it shows a consistent ratio in $y$-values, indicating an exponential function.

Would you like further details or have any questions?

Here are five related questions to expand on this:

1. How do you identify a linear function from a table of values?
2. What is the difference between linear and exponential growth?
3. How can you use a table of values to find an exponential equation?
4. What are real-life examples of exponential functions?
5. How do you determine if a function is quadratic based on a table of values?

Tip: In exponential functions, a consistent ratio (multiplication factor) between consecutive $y$-values usually signifies the presence of exponential growth or decay.