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_1

Step2: Analyze the graph

Looking at the parabola (since it is a quadratic - like graph). The vertex of the parabola (the highest point) is at \(x = 3\). For a parabola opening downwards (the coefficient of \(x^{2}\) is negative), the function is increasing to the left of the vertex.

Answer:

The function is increasing on the interval \((-\infty,3)\)