Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Recall the definition 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 the interval with \(x_1

Step2: Analyze the graph

Looking at the parabola (since the graph is a U - shaped curve, it is a quadratic function). The vertex of the parabola is the point where the function changes from increasing to decreasing or vice - versa. For a parabola opening downwards (as this one does, since the ends go down), the function is increasing to the left of the vertex and decreasing to the right of the vertex.
From the graph, the vertex is at \(x = 4\).

Answer:

The function is decreasing on the interval \((4,\infty)\)