Question

determine the domain on which the following function is increasing.
answer attempt 1 out of 2

Explanation:

Step1: Identify the vertex's x - coordinate

The graph is a parabola opening downward (since the ends point down). The vertex is the highest point. From the graph, the vertex is at \(x = 1\) (by looking at the grid, the peak is above \(x = 1\)).

Step2: Determine the increasing interval

A downward - opening parabola increases to the left of its vertex (since as \(x\) increases towards the vertex, \(y\) increases). So, the function is increasing when \(x\) is less than \(1\), that is, for all real numbers \(x\) such that \(x<1\) or in interval notation \((-\infty, 1)\).

Answer:

The function is increasing on the interval \((-\infty, 1)\) (or \(x < 1\))