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 that interval with \(x_1

Step2: Analyze the graph

Looking at the parabola (quadratic function graph), we observe that as \(x\) values increase from \(-\infty\) to the vertex \(x -\) coordinate, the \(y -\) values of the function are getting smaller.
The vertex of the parabola (from the graph) has an \(x -\) coordinate of \(2\).
So, for \(x\in(-\infty, 2)\), if \(x_1

Answer:

The function is decreasing on the interval \((-\infty,2)\)