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The image shows a question asking which statement is true about the function \( q \) based on the given data table. The table shows the values of \( q(x) \) for different values of \( x \), and you need to determine the nature of the function \( q(x) \).

### Given Data:
\[
\begin{array}{c|c}
x & q(x) \\
\hline
1 & 9 \\
2 & 27 \\
3 & 81 \\
4 & 243 \\
\end{array}
\]

### Observations:
1. When \( x = 1 \), \( q(x) = 9 \).
2. When \( x = 2 \), \( q(x) = 27 \).
3. When \( x = 3 \), \( q(x) = 81 \).
4. When \( x = 4 \), \( q(x) = 243 \).

### Analyzing the Function:
- **Constant Ratio Test**: Let's check if the function is exponential by determining if there's a constant ratio between successive values of \( q(x) \).
  
  - \( \frac{q(2)}{q(1)} = \frac{27}{9} = 3 \)
  - \( \frac{q(3)}{q(2)} = \frac{81}{27} = 3 \)
  - \( \frac{q(4)}{q(3)} = \frac{243}{81} = 3 \)

  Since the ratio between successive terms is constant (3), the function is exponential.

### Conclusion:
The correct statement is:

**D. Function q is exponential because q(x) changes by a constant factor per unit interval.**

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**Do you have any further questions or would you like more details on this? Here are some related questions to explore:**

1. What defines an exponential function mathematically?
2. How does an exponential function differ from a linear function in terms of growth?
3. What is the general form of an exponential function?
4. How can you identify an exponential function from a table of values?
5. How do you determine the base of an exponential function from its table of values?
6. What are some real-life examples of exponential growth or decay?
7. How does the graph of an exponential function differ from that of a linear or quadratic function?
8. What is the significance of the constant factor in an exponential function?

**Tip:** When identifying an exponential function, look for a constant multiplicative factor between consecutive values of the function, rather than a constant difference, which indicates a linear function.

Learn how to identify exponential functions by analyzing function q based on given data. Understand the constant ratio test and its application in determining if a function is exponential. Suitable for Grades 9-12 students studying functions and algebra.

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