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

검증된 단계별 안내

Step 1: Identify the relation shown on the graph. The graph depicts an oval shape, which is a closed curve representing a set of points (x, y).

Step 2: Determine if the relation defines a function by using the Vertical Line Test. This test states that if any vertical line intersects the graph at more than one point, the relation is not a function.

Step 3: Apply the Vertical Line Test to the oval. Notice that vertical lines passing through the middle of the oval intersect the graph at two points, meaning for some x-values there are two corresponding y-values.

Step 4: Conclude that the relation is not a function because it fails the Vertical Line Test (some x-values correspond to multiple y-values).

Step 5: Find the domain and range by looking at the extent of the oval along the x-axis and y-axis. The domain is the set of all x-values covered by the oval, and the range is the set of all y-values covered by the oval.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means no vertical line intersects the graph at more than one point, ensuring each x has a unique y.

Domain of a Relation

The domain is the set of all possible input values (x-values) for the relation. It includes every x-coordinate that appears on the graph, representing all values for which the relation is defined.

Range of a Relation

The range is the set of all possible output values (y-values) for the relation. It includes every y-coordinate that appears on the graph, representing all values the relation can produce.