Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Recall the definition of an 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 graph, from \(x = 0\) to \(x=3\) (assuming the vertex is at \(x = 3\) based on the shape of the parabola - like curve), as \(x\) increases, \(y\) also increases.

Answer:

The function is increasing on the interval \((-\infty,3)\) (assuming the vertex \(x -\) coordinate is \(3\) from the graph's shape. If we consider the grid - like background (each square as \(1\) unit), from \(x = 0\) to \(x=3\), the function is rising. So the domain on which the function is increasing is \([0,3]\) (if we assume the left - most point of the function's domain is \(x = 0\) as it starts from \(y-\) axis). But if we consider the general concept of the interval where the function is rising (before the vertex), it is \((-\infty,3)\) (assuming the function is defined for all \(x\) before the vertex in the context of the graph's trend. If we assume the function starts at \(x = 0\) (since it touches the \(y-\) axis at \(x = 0\)), then it is \([0,3]\))