Identify the Decreasing Domain of f(x): Graph Analysis

In which domain does the function decrease?

To solve this problem, we'll examine each interval provided between the points for $f(x)$ from the graph, checking where $\ f(x)$ decreases:

• Step 1: Look at the interval $2 < x < 3$.
  - For $x = 2$, $\ f(x) = 15$ and for $x = 3$, $\ f(x) = 0$.
  - Since $15 \to 0$ as $x$ moves from 2 to 3, the function decreases. Thus, this interval is decreasing.
• Step 2: Examine the interval $x > 3.5$.
  - For $x = 3.5$, $\ f(x) = 2$ at the starting point, and it decreases beyond this point.
  - Since we need to find where $f(x)$ decreases, and the function decreases as it's moving towards a lower value from this point, this indeed indicates a decreasing domain.

Therefore, the intervals where the function decreases are $2 < x < 3$ and $x > 3.5$.

The solution to this problem is that Answers B and C are correct, identifying the domains where $f(x)$ decreases.