Questions: Determine whether the relation defines a function, and give the domain and range. Is this the graph of a function? A. No, because every vertical line intersects the graph of a relation in no more than one point. B. No, because at least one vertical line intersects the graph more than once. C. Yes, because every vertical line intersects the graph of a relation in no more than one point. D. Yes, because at least one vertical line intersects the graph of a relation in no more than one point. What is the domain of the relation? (Type your answer in interval notation.) What is the range of the relation? (Type your answer in interval notation.)

Determine whether the relation defines a function, and give the domain and range.

Is this the graph of a function?
A. No, because every vertical line intersects the graph of a relation in no more than one point.
B. No, because at least one vertical line intersects the graph more than once.
C. Yes, because every vertical line intersects the graph of a relation in no more than one point.
D. Yes, because at least one vertical line intersects the graph of a relation in no more than one point.

What is the domain of the relation?
(Type your answer in interval notation.)
What is the range of the relation?
(Type your answer in interval notation.)

Transcript text: Determine whether the relation defines a function, and give the domain and range. Is this the graph of a function? A. No, because every vertical line intersects the graph of a relation in no more than one point. B. No, because at least one vertical line intersects the graph more than once. C. Yes, because every vertical line intersects the graph of a relation in no more than one point. D. Yes, because at least one vertical line intersects the graph of a relation in no more than one point. What is the domain of the relation? $\square$ (Type your answer in interval notation.) What is the range of the relation? $\square$ (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Determine if the graph is a function

The given graph is not a function. This is because some vertical lines intersect the circle at two points. For example, the vertical line x=1 intersects the circle at y=1 and y=-1. This violates the vertical line test, which states that a graph represents a function if and only if every vertical line intersects the graph at most once.

Step 2: Determine the domain of the relation

The domain of the relation is the set of all possible x-values. In the graph, the x-values span from -2 to 2, inclusive. In interval notation, this is written as [-2, 2].

Step 3: Determine the range of the relation

The range of the relation is the set of all possible y-values. In the graph, the y-values span from -2 to 2, inclusive. In interval notation, this is written as [-2, 2].