To determine if a graph represents a function, you can use the Vertical Line Test. This test states that if you can draw a vertical line anywhere on the graph and it intersects the graph at more than one point, then the graph does not represent a function.
A function, by definition, is a relation where each input (x-coordinate) is associated with exactly one output (y-coordinate). This means that for every x-value, there should be only one corresponding y-value. So, if a vertical line crosses the graph at multiple points, it indicates that there are multiple outputs for that single input, violating the definition of a function.
For example, consider a circle. If you draw a vertical line through any point where the circle is present, you will find that the line intersects the circle at two points. Hence, it does not satisfy the vertical line test, and therefore, a circle does not represent a function.
On the other hand, a straight line with a positive or negative slope will pass the vertical line test because every vertical line will intersect it at exactly one point. Thus, that line represents a function.