Let's analyze the three functions in the table to determine their types:

Function 1

• $x = 5$, $y = 768$
• $x = 6$, $y = 192$
• $x = 7$, $y = 48$
• $x = 8$, $y = 12$
• $x = 9$, $y = 3$

Each time $x$ increases by 1, $y$ is divided by 4. This shows a constant multiplicative change, which is characteristic of an exponential function.

Function 2

• $x = 1$, $y = -14$
• $x = 2$, $y = -9$
• $x = 3$, $y = -6$
• $x = 4$, $y = -5$
• $x = 5$, $y = -6$

Here, the differences between consecutive $y$-values are not constant. The first differences are: $-9 - (-14) = 5$, $-6 - (-9) = 3$, $-5 - (-6) = 1$, and so on. Since the second differences are constant, this suggests that the function is quadratic.

Function 3

• $x = 2$, $y = -11$
• $x = 3$, $y = -13$
• $x = 4$, $y = -17$
• $x = 5$, $y = -23$
• $x = 6$, $y = -31$

The differences between consecutive $y$-values are: $-13 - (-11) = -2$, $-17 - (-13) = -4$, $-23 - (-17) = -6$, and $-31 - (-23) = -8$. Since the differences are constant and linear, this is a linear function.

Conclusion:

1. Function 1: Exponential
2. Function 2: Quadratic
3. Function 3: Linear

Would you like more details or explanations on these function types? Here are five questions to explore:

1. How can you determine a function is quadratic from its table?
2. What is the general form of an exponential function?
3. How do you differentiate between exponential and linear functions using a table of values?
4. What are second differences in relation to quadratic functions?
5. How does knowing the type of function help in graphing it?

Tip: Always check for constant differences (for linear), constant second differences (for quadratic), and multiplicative patterns (for exponential) when analyzing tables of values.