Questions: reach graph below, state whether it represents a function. Function? Graph 1

Solution Steps

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

Since we cannot visually inspect the graph in this text-based format, we will assume the graph data is provided in a list of coordinate points. We will write a Python function to check if any x-coordinate is repeated with different y-coordinates.

1. Extract the x-coordinates from the list of points.
2. Check if any x-coordinate appears more than once with different y-coordinates.

Given the set of points \( (1, 2), (2, 3), (3, 4), (1, 5) \), we need to determine if this set represents a function. A relation is a function if each input (x-coordinate) corresponds to exactly one output (y-coordinate).

In the provided points, we observe that the x-coordinate \( 1 \) appears twice:

• For \( x = 1 \), the corresponding y-values are \( 2 \) and \( 5 \).

This means that the same x-coordinate maps to two different y-values, violating the definition of a function.

Since the vertical line test fails (as a vertical line at \( x = 1 \) would intersect the graph at two points), we conclude that the relation does not represent a function.

Final Answer