Question

use the vertical line test to determine whether the graph to the right is the graph of a function. find the domain and the range of the relation. is this the graph of a function? no yes the domain is (type your answer in interval notation.)

Explanation:

Step1: Vertical Line Test

A graph represents a function if no vertical line intersects the graph more than once. For the given circle, a vertical line (e.g., \(x = 0\) or \(x = 1\)) will intersect the circle at two points, so it is not a function. So the answer to "Is this the graph of a function?" is No.

Step2: Find Domain

The circle is centered, and from the graph (assuming grid squares are 1 unit), the leftmost \(x\)-value is \(-2\) and the rightmost is \(4\). So the domain (all \(x\)-values) is from \(-2\) to \(4\), in interval notation \([-2, 4]\).

Step3: Find Range (though not fully asked, but for domain we focus on \(x\)-values)

The domain is the set of all \(x\)-coordinates of the points on the graph. The circle extends horizontally from \(x=-2\) to \(x = 4\), so domain is \([-2, 4]\).

Answer:

Is this the graph of a function? No
The domain is \([-2, 4]\)