I can do it from a graph, but given just a table of values I end up guessing.
Accepted answer
Check what stays **constant** as the input steps up by a fixed amount.
- **Linear** — constant *differences* in the output. `2, 5, 8, 11` adds 3 each time.
- **Exponential** — constant *ratios* in the output. `2, 6, 18, 54` multiplies by 3 each time.
So: subtract consecutive outputs; if that's constant, linear. If not, divide consecutive outputs; if that's constant, exponential.
**Logarithmic** flips the roles: the *input* multiplies by a constant factor while the output changes by a constant difference. If `x = 1, 10, 100, 1000` gives `y = 0, 1, 2, 3`, that's logarithmic — it's the inverse pattern of exponential, which is exactly why the two are inverse functions.