Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Understand increasing function

A function is increasing on an interval if, as \( x \) increases, \( y \) also increases. Visually, this is where the graph rises from left to right.

Step2: Analyze the graph

The graph starts at \( (0, 28) \) (since the leftmost point is on the y - axis at \( x = 0 \)) and rises until it reaches the vertex (the peak) at \( x = 3 \) (by looking at the x - coordinate of the highest point on the graph). After \( x = 3 \), the graph starts to fall. The domain of the function (the x - values it covers) starts at \( x = 0 \) (the left - most point) and ends at \( x = 9 \) (the right - most point, a closed dot). But the increasing part is from \( x = 0 \) to \( x = 3 \) (or more precisely, from the starting x - value to the x - value of the vertex). Looking at the x - axis, the starting x is \( 0 \) (since the graph starts at \( (0,28) \)) and the vertex is at \( x = 3 \) (by counting the grid squares: from \( x = 0 \) to \( x = 3 \), the graph is rising). So the function is increasing on the interval \( [0, 3] \) (or in terms of the domain from \( x = 0 \) to \( x = 3 \), considering the graph's start at \( x = 0 \) and peak at \( x = 3 \)). Wait, actually, let's check the x - coordinates again. The left - most point is at \( x = 0 \) (the y - intercept), and the graph increases until it reaches the maximum at \( x = 3 \) (because from \( x = 0 \) to \( x = 3 \), as x increases, y increases; after \( x = 3 \), y decreases). The right - most point is at \( x = 9 \), but the increasing part is from the minimum x (0) to the x of the maximum (3). So the domain on which the function is increasing is \( 0\leq x\leq3 \) (or in interval notation \( [0, 3] \)).

Answer:

The function is increasing on the domain \( [0, 3] \) (or \( 0\leq x\leq3 \))