Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Recall increasing - function property

A function $y = f(x)$ is increasing when, as $x$ increases, $y$ also increases. On a graph, the function has a positive - slope.

Step2: Analyze the given graph

Looking at the graph of the function, we see that as $x$ moves from negative infinity to some value (the $x$ - coordinate of the vertex), the $y$ - values of the function are getting larger.

Step3: Identify the domain

The vertex of the parabola (assuming it's a parabola) is at $x=-2$. The function is increasing for $x$ values from negative infinity to $-2$. In interval notation, the domain on which the function is increasing is $(-\infty,-2)$.

Answer:

$(-\infty,-2)$