Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Understand the concept of increasing function

A function \(y = f(x)\) is increasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1eq0\)), if \(a<0\) (opens down - like the given graph), it is increasing to the left of the vertex.

Step2: Locate the vertex of the parabola

By observing the graph, the vertex (the highest point for a parabola opening down) has an \(x\) - coordinate. The vertex of the parabola in the graph is at \(x = 2\).

Step3: Determine the increasing interval

Since the parabola opens down (\(a<0\)), the function is increasing for \(x\) values less than the \(x\) - coordinate of the vertex.

Answer:

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