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: Analyze the given graph

Looking at the graph, we can see that after the vertex (the highest point of the graph), the function starts to decrease. The \(x\) - coordinate of the vertex is \(x = 7\). As \(x\) increases beyond \(7\), the \(y\) - values of the function decrease. The function is defined from \(x = 0\) (since the \(y\) - intercept is at \(x = 0\)) to \(x=14\) (the \(x\) - intercept).

Answer:

The function is decreasing on the interval \([7,14]\)