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 given graph

Looking at the graph, we start from the left - most point (in the domain of the function). As we move from left - to - right, the function rises until it reaches the vertex (the highest point of the parabola - like graph).
The vertex of the graph (the point where the function changes from increasing to decreasing) occurs at \(x = 3\).
For \(x\) values from \(x = 0\) (the left - most point of the function's non - negative \(x\) domain, since the function starts at \((0,50)\)) to \(x = 3\), as \(x\) increases, \(y\) also increases.

Answer:

The function is increasing on the interval \([0,3]\)