Question

determine the range of the following graph:

Explanation:

Step1: Identify the minimum and maximum y - values

The range of a graph is the set of all possible y - values (outputs) of the function. From the graph, we can see that the lowest point (minimum y - value) is at \(y=-9\) (the vertex at \(x = 0\)) and the highest points: one at \(x=-2\) with \(y = 1\) and another peak at \(x = 4\) with \(y=1\), and the other endpoint at \(x = 6\) with \(y=-9\)? Wait, no, let's re - examine. Wait, the left endpoint is at \(x=-2,y = 1\), the bottom point is at \(x = 0,y=-9\), the peak is at \(x = 4,y = 1\), and the right endpoint is at \(x = 6,y=-9\)? Wait, no, looking at the graph: the leftmost point is a blue dot at \(x=-2,y = 1\), then the graph goes down to a minimum at \(y=-9\) (around \(x = 0\)), then up to a peak at \(y = 1\) (around \(x = 4\)), then down to a blue dot at \(x = 6,y=-9\)? Wait, no, the y - coordinate of the right endpoint: looking at the grid, the right dot is at \(x = 6\), and its y - value is \(-9\)? Wait, no, the minimum y - value is \(-9\) (the lowest point of the graph), and the maximum y - value is \(1\) (the y - value of the two endpoints and the peak). So the range is all real numbers \(y\) such that \(-9\leq y\leq1\).

Step2: Express the range

The range of a function is the interval of y - values from the minimum to the maximum. So the range is \([-9,1]\) (since the graph includes the endpoints, as the dots are filled, meaning the function includes those points).

Answer:

\(-9\leq y\leq1\) (or in interval notation \([-9, 1]\))