Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Understand the concept of a decreasing function

A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in that interval with \(x_1

Step2: Identify the vertex of the function

The vertex of the given parabola (since it has a single maximum point) is the point where the function changes from increasing to decreasing. From the graph, the \(x\) - coordinate of the vertex is \(x = 6\).

Step3: Determine the decreasing interval

For a parabola opening downwards (which is the case here as the function has a maximum), the function is decreasing for \(x\) values greater than the \(x\) - coordinate of the vertex.

Answer:

The function is decreasing on the interval \([6,13]\)