Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Recall increasing - function concept

A function is increasing when the y - values increase as the x - values increase.

Step2: Observe the graph

Looking at the graph of the parabola, we see that as x moves from negative infinity to the vertex x - coordinate, the function value y is increasing.

Step3: Identify the vertex x - coordinate

The vertex of the parabola is at \(x = 3\) (by visual inspection of the graph). So the function is increasing for \(x\in(-\infty,3)\).

Answer:

\((-\infty,3)\)