Bot GPT 4-o mini To determine which relation is a function, we need to apply the vertical line test. A relation is a function if every x-value is associated with exactly one y-value. This means that no vertical line drawn on the graph can intersect the graph at more than one point.
Let's analyze the provided graphs based on the points given:
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First Graph: The points are:
- (-4, 3)
- (-2, 1)
- (-1, 3)
- (-1, -1)
- (1, 1)
- (2, -1)
The x-value -1 corresponds to two different y-values (3 and -1), which violates the definition of a function. This relation is not a function.
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Second Graph: The points are:
- (-2, 1)
- (-2, -2)
- (-1, 3)
- (0, 1)
- (2, 0)
- (2, -2)
Here, the x-value -2 corresponds to two different y-values (1 and -2), and the x-value 2 also corresponds to two different y-values (0 and -2). This relation is not a function.
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Third Graph: The points are:
- (-2, 1)
- (-1, 3)
- (0, 2)
- (0, -1)
- (1, 3)
- (2, 1)
The x-value 0 corresponds to two different y-values (2 and -1), which violates the definition of a function. This relation is not a function.
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Fourth Graph: The points are:
- (-3, -1)
- (-2, 3)
- (0, -3)
- (1, -2)
- (2, 2)
- (3, 0)
All x-values are unique, with each corresponding to a single y-value. Therefore, this relation does satisfy the condition of a function. This relation is a function.
In conclusion, the fourth graph is the one that represents a function.
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