Here’s the solution for each part of the assessment:

1. Graph with the curved line:

   • Type: Exponential
   • Reason: Exponential functions show a constant ratio between consecutive values, represented by the steep upward curve.

2. Table labeled $g(x)$:

   • Type: Linear
   • Reason: The differences between $g(x)$ values are constant ($-8, -5, -2, 1, 4, 7$), showing a constant difference.

3. Table labeled $f(x)$:

   • Type: Exponential
   • Reason: The $f(x)$ values double each time (e.g., $6 \to 12 \to 24 \to 48$), showing a constant ratio.

4. Equation $y = -2x + 8$:

   • Type: Linear
   • Reason: Linear equations have the form $y = mx + b$ with a constant rate of change ($-2$ here).

5. Recurrence relation $f(n) = f(n-1) + 4$:

   • Type: Linear
   • Reason: Adding a constant value ($+4$) for every step results in a constant difference.

6. Equation $f(x) = 3(2^x)$:

   • Type: Exponential
   • Reason: The function has a base of $2$ raised to a power ($x$), showing exponential growth with a constant ratio.

Would you like further details or help with any specific part of this solution?

Here are 5 related questions to expand your understanding:

1. What is the general difference between linear and exponential functions?
2. How can you verify whether a table shows a linear or exponential function?
3. What happens when the base of an exponential function is less than 1?
4. How would you describe the graph of a negative linear slope like $y = -2x + 8$?
5. Can a recurrence relation represent an exponential function? If so, how?

Tip: To quickly identify an exponential pattern, check for a consistent multiplication factor (constant ratio) between outputs!