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

Video Solution

Solution Steps

00:00 Find the domain of decrease of the function

00:04 The function decreases when X values increase and Y values decrease

00:11 From this point the function begins to decrease

00:14 At this point it rises again, and then decreases back

00:21 We can conclude from this the domain of decrease

00:28 And this is the solution to the question

Step-by-Step Solution

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.