Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Recall the concept of 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 graph of the function (a parabola - like curve), we observe the direction of the curve. The curve is going downwards (from left - to - right) for \(x\) values from \(-\infty\) to the \(x\) - coordinate of the vertex.
Assume the vertex of the parabola - like curve has \(x\) - coordinate \(x = 1\) (by visual inspection of the graph).

Answer:

\((-\infty,1)\)