Let's analyze the table to determine whether the function is linear, exponential, or neither. Here's the data provided:

Step 1: Check for Linearity

A linear function has a constant rate of change (difference between successive $f(x)$ values).

• Between $x = -1$ and $x = 0$: $f(x) = 5 - 3 = 2$
• Between $x = 0$ and $x = 1$: $f(x) = 10 - 5 = 5$
• Between $x = 1$ and $x = 2$: $f(x) = 15 - 10 = 5$
• Between $x = 2$ and $x = 3$: $f(x) = 25 - 15 = 10$

The differences are not constant. Therefore, the function is not linear.

Step 2: Check for Exponentiality

An exponential function has a constant ratio between successive $f(x)$ values.

• Ratio between $x = -1$ and $x = 0$: $5 / 3 \approx 1.67$
• Ratio between $x = 0$ and $x = 1$: $10 / 5 = 2$
• Ratio between $x = 1$ and $x = 2$: $15 / 10 = 1.5$
• Ratio between $x = 2$ and $x = 3$: $25 / 15 \approx 1.67$

The ratios are not constant. Therefore, the function is not exponential.

Step 3: Conclusion

The function is neither linear nor exponential.

Would you like further assistance or more examples related to this topic?

Here are 5 follow-up questions you might find useful:

1. How do you formally derive equations for functions that are neither linear nor exponential?
2. Can the given data represent a quadratic function? How can we verify this?
3. What methods can be used to approximate non-linear and non-exponential data?
4. How do you graph a set of values like this to analyze its behavior visually?
5. What are other types of functions that can model this data?

Tip: When analyzing a function, always check for constant differences or ratios first to simplify your work.