determine the domain on which the following function is increasing.

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Accepted Answer

# 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 that interval with $x_1<x_2$, we have $f(x_1)<f(x_2)$. For a parabola $y = ax^{2}+bx + c$ ($a<0$), it is increasing on the interval $(-\infty,-\frac{b}{2a})$ (using the vertex formula $x =-\frac{b}{2a}$). In the case of a graph (visual method), we look at the part of the graph where as $x$ increases, $y$ also increases.
## Step2: Analyze the given graph
The given graph is a parabola opening downwards (since it has a maximum - point). The function is increasing from the left - hand side up to the $x$ - coordinate of the vertex.

# Answer:
The function is increasing on the interval $(-\infty,x_{\text{vertex}})$ (where $x_{\text{vertex}}$ is the $x$ - coordinate of the vertex of the parabola). If we assume the vertex $x$ - value is $h$ (from the graph's symmetry), the domain on which the function is increasing is $(-\infty,h)$ (visually, from the left - most part of the graph up to the point where the function starts to decrease).

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Question

Explanation:

Step1: Recall the concept of increasing function

Step2: Analyze the given graph

Answer: