1. The problem is to determine where the function $f(x)$ is increasing or decreasing based on given values of $x$ and $f(x)$ in a table. 2. A function is increasing on an interval if for any two points $x_1 < x_2$, we have $f(x_1) < f(x_2)$. 3. Similarly, a function is decreasing on an interval if for any two points $x_1 < x_2$, we have $f(x_1) > f(x_2)$. 4. To analyze the function, look at the values of $f(x)$ as $x$ increases and note where $f(x)$ goes up (increasing) or down (decreasing). 5. For example, if the table is: | $x$ | 1 | 2 | 3 | 4 | 5 | |-----|---|---|---|---|---| | $f(x)$ | 2 | 4 | 3 | 5 | 7 | 6. From $x=1$ to $x=2$, $f(x)$ goes from 2 to 4 (increasing). 7. From $x=2$ to $x=3$, $f(x)$ goes from 4 to 3 (decreasing). 8. From $x=3$ to $x=5$, $f(x)$ goes from 3 to 7 (increasing). 9. So the function is increasing on intervals $(1,2)$ and $(3,5)$ and decreasing on $(2,3)$. 10. This method applies to any table of values: compare consecutive $f(x)$ values to find increasing or decreasing intervals.