To determine whether the function is linear, exponential, or neither, we will analyze the table data step-by-step.

Table:

$x$	$f(x)$
$-1$	1
$0$	2
$1$	4
$2$	6
$3$	10

Step 1: Check for linearity

A linear function has a constant difference between consecutive $f(x)$ values when $x$ increases by 1.

1. From $x = -1$ to $x = 0$: $f(0) - f(-1) = 2 - 1 = 1$
2. From $x = 0$ to $x = 1$: $f(1) - f(0) = 4 - 2 = 2$
3. From $x = 1$ to $x = 2$: $f(2) - f(1) = 6 - 4 = 2$
4. From $x = 2$ to $x = 3$: $f(3) - f(2) = 10 - 6 = 4$

The differences are not constant ($1, 2, 4$), so the function is not linear.

Step 2: Check for exponential behavior

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

1. From $x = -1$ to $x = 0$: $\frac{f(0)}{f(-1)} = \frac{2}{1} = 2$
2. From $x = 0$ to $x = 1$: $\frac{f(1)}{f(0)} = \frac{4}{2} = 2$
3. From $x = 1$ to $x = 2$: $\frac{f(2)}{f(1)} = \frac{6}{4} = 1.5$
4. From $x = 2$ to $x = 3$: $\frac{f(3)}{f(2)} = \frac{10}{6} \approx 1.67$

The ratios are not constant ($2, 1.5, 1.67$), so the function is not exponential.

Conclusion:

Since the function is neither linear nor exponential, the correct answer is:

C. The function is neither linear nor exponential.

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Follow-Up Questions:

1. Would you like to analyze if this function could fit another type of model?
2. Do you need help visualizing the data with a graph?
3. Should we explore potential polynomial fits for this data?
4. Do you need step-by-step guidance on identifying non-linear functions?
5. Would you like me to explain why constant differences and ratios define linear and exponential functions?

Tip:

When analyzing a table of values, always calculate both first differences (for linearity) and ratios (for exponential growth) to identify the type of function.