The image contains a table with a function represented by $x$ and $f(x)$ values, as well as some questions related to the function's domain, type, and characteristics. Here's what we can analyze:

Table of Function Values:

Questions from the worksheet:

1. Domain and whether the function is discrete or continuous:

   • The domain consists of the specific $x$-values in the table: $\{-130, -124, -120, -114, -110, -107, -100\}$.
   • Since the function only takes on these distinct values and does not cover all values in a range, this function is discrete. This is confirmed by the handwritten answer "discrete" in the image.

2. Type of function and the difference or growth factor:

   • The function appears to show a decreasing pattern in $f(x)$ as $x$ increases. To determine if it's arithmetic (linear) or geometric (exponential), we can calculate the differences between consecutive $f(x)$ values:
     • $57.2 - 54.56 = 2.64$
     • $54.56 - 52.8 = 1.76$
     • $52.8 - 50.16 = 2.64$
     • $50.16 - 48.4 = 1.76$
     • $48.4 - 47.08 = 1.32$
     • $47.08 - 44 = 3.08$

   The differences vary slightly, so this function is not strictly linear. It doesn't follow a constant ratio, so it's not geometric either. It seems to be an approximation of a decreasing pattern, likely not an exact arithmetic or geometric sequence.

Would you like me to provide more detailed calculations or assist with another part of the problem?

Here are 5 follow-up questions related to this:

1. Would you like to explore the specific type of pattern this function might follow?
2. Should we graph the function to analyze its trend?
3. Would you like to calculate the rate of change between other points to see if the pattern stabilizes?
4. How would you describe the behavior of this function based on the values?
5. Do you want to examine possible real-world applications for such a function?

Tip: When trying to identify if a function is arithmetic, calculate the first differences between consecutive terms. For geometric, calculate the ratio between consecutive terms.