For each graph, determine whether y is a function of x. Give the domain and range of each relation.

검증된 단계별 안내

Step 1: Identify if y is a function of x by using the vertical line test. If any vertical line intersects the graph at more than one point, then y is not a function of x.

Step 2: Observe the graph carefully. Notice that for each x-value, there is exactly one corresponding y-value. This means the graph passes the vertical line test, so y is a function of x.

Step 3: Determine the domain by looking at the x-values covered by the graph. The graph starts from approximately x = -20 and extends to the right indefinitely, so the domain is \([-20, \infty)\).

Step 4: Determine the range by looking at the y-values covered by the graph. The graph starts from about y = -15 and goes up to y = 30, then continues horizontally at y = 30, so the range is \([-15, 30]\).

Step 5: Summarize: y is a function of x, with domain \([-20, \infty)\) and range \([-15, 30]\).

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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. Understanding this helps determine if y is a function of x by checking if each x has a unique y.

Domain and Range

The domain is the set of all possible x-values for which the function or relation is defined. The range is the set of all possible y-values that the function or relation can take. Identifying these sets helps describe the behavior and limits of the graph.

Vertical Line Test

The vertical line test is a visual method to determine if a graph represents a function. If any vertical line drawn through the graph intersects it more than once, the graph does not represent a function. This test is essential for analyzing the given graph.