Questions: For each graph below, state whether it represents a function.

Solution Steps

To determine if a graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

For Graph 1, the points are given as \( \{1: [2], 2: [3], 3: [4]\} \). Each x-coordinate corresponds to a unique y-coordinate. Therefore, it passes the vertical line test, indicating that it represents a function.

For Graph 2, the points are \( \{1: [2, 3], 2: [3], 3: [4]\} \). The x-coordinate \( 1 \) corresponds to two different y-coordinates \( 2 \) and \( 3 \). This means that a vertical line at \( x = 1 \) would intersect the graph at two points, failing the vertical line test. Thus, Graph 2 does not represent a function.

For Graph 3, the points are \( \{1: [2], 2: [3], 3: [4, 5]\} \). The x-coordinate \( 3 \) corresponds to two different y-coordinates \( 4 \) and \( 5 \). Similar to Graph 2, a vertical line at \( x = 3 \) would intersect the graph at two points, failing the vertical line test. Therefore, Graph 3 does not represent a function.

Final Answer