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 the interval with \(x_1

Step2: Analyze the graph

For a parabola \(y = ax^{2}+bx + c\) (the given graph is a parabola, \(a>0\) since it opens upwards), the vertex form is \(y=a(x - h)^{2}+k\). The axis of symmetry is \(x = h\). For a parabola \(y = ax^{2}+bx + c\), the axis of symmetry is \(x=-\frac{b}{2a}\).
Looking at the graph, we can observe that the vertex (the minimum point of the parabola) occurs at \(x = 3\).
To the left of \(x = 3\) (i.e., \(x<3\)), the function is decreasing (the graph falls from left - to - right). To the right of \(x = 3\) (i.e., \(x>3\)), the function is increasing (the graph rises from left - to - right).

Answer:

\((3,\infty)\)