Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Recall 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 that interval with \(x_1

Step2: Analyze the given graph

The given graph is a parabola opening downwards (since it has a maximum - point). The function is increasing from the left - hand side up to the \(x\) - coordinate of the vertex.

Answer:

The function is increasing on the interval \((-\infty,x_{\text{vertex}})\) (where \(x_{\text{vertex}}\) is the \(x\) - coordinate of the vertex of the parabola). If we assume the vertex \(x\) - value is \(h\) (from the graph's symmetry), the domain on which the function is increasing is \((-\infty,h)\) (visually, from the left - most part of the graph up to the point where the function starts to decrease).