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We are asked to identify which of the given relations are functions. A relation is a function if each input (x-value) has only one output (y-value). We are given two sets of ordered pairs and two graphs.

AlgebraFunctionsRelationsVertical Line TestOrdered PairsFunction Identification
2025/4/9

1. Problem Description

We are asked to identify which of the given relations are functions. A relation is a function if each input (x-value) has only one output (y-value). We are given two sets of ordered pairs and two graphs.

2. Solution Steps

a) The relation is {(-2,-1), (-1,2), (0,1), (-1,3)}.
We check if any x-value is repeated with different y-values. The x-value -1 is paired with both 2 and

3. Therefore, this relation is not a function.

b) The relation is {(-2,-1), (-1,-1), (0,1), (1,0)}.
We check if any x-value is repeated with different y-values. Each x-value is unique: -2, -1, 0,

1. Therefore, this relation is a function.

c) We need to apply the vertical line test. If any vertical line intersects the graph at more than one point, then the relation is not a function. Visualizing vertical lines intersecting the graph, we see that any vertical line will intersect the graph at most once. Therefore, this relation is a function.
d) We need to apply the vertical line test. If any vertical line intersects the graph at more than one point, then the relation is not a function. Visualizing vertical lines intersecting the graph, we can find a vertical line that intersects the graph at two points (for example, a vertical line slightly to the right of the y-axis). Therefore, this relation is not a function.

3. Final Answer

The relations that are functions are b) and c).

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