Question

identify the interval where the function is decreasing.
5 < x < 12
6 < x < 12
1 < x < 6
1 < x < 5

Explanation:

Step1: Understand function increasing/decreasing

A function is decreasing when, as \(x\) increases, \(y\) decreases.

Step2: Analyze the graph

Looking at the graph, from \(x = 6\) to \(x = 12\), as \(x\) values increase, the \(y\) - values of the function decrease.
For \(1 < x < 6\), the function is increasing (as \(x\) increases, \(y\) increases). For \(5 < x < 12\), the interval \(5 < x < 6\) has the function increasing. For \(1 < x < 5\), the function is increasing. Only for \(6 < x < 12\) does the function show a decreasing trend (as \(x\) moves from \(6\) to \(12\), \(y\) values go down).

Answer:

B. \(6 < x < 12\)