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 of the function

For a parabola (quadratic function) \(y = ax^{2}+bx + c\) (the given graph is a parabola), its vertex form is \(y=a(x - h)^{2}+k\). The axis of symmetry is \(x = h\).
If \(a>0\) (the parabola opens upwards as in the given graph), the function is decreasing on the interval \((-\infty,h)\) and increasing on the interval \((h,\infty)\).
From the graph, the vertex (the point where the function changes from decreasing to increasing) has \(x\) - coordinate \(x = 1\).

So the function is decreasing on the interval \((-\infty,1)\).

Answer:

$(-\infty,1)$