Question

12.
domain:
range:

Explanation:

Step1: Determine the Domain

The domain of a graph is the set of all x - values (horizontal axis) that the graph covers. Looking at the ellipse, the leftmost point is at \(x=-3\) and the rightmost point is at \(x = 3\) (assuming each grid square has a side length of 1 unit). So the domain is all real numbers \(x\) such that \(-3\leq x\leq3\).

Step2: Determine the Range

The range of a graph is the set of all y - values (vertical axis) that the graph covers. The bottommost point of the ellipse is at \(y=-3\) and the topmost point is at \(y = 1\) (by looking at the vertical grid lines). So the range is all real numbers \(y\) such that \(-3\leq y\leq1\).

Answer:

Domain: \(-3\leq x\leq3\) (or in interval notation \([-3,3]\))
Range: \(-3\leq y\leq1\) (or in interval notation \([-3,1]\))