How can we determine from a graph if a function is shown or not?
If you have a graph and you want to determine if a function is shown or not, you can use the vertical line test.
The vertical line test states that a graph represents a function if every vertical line you can draw on the graph intersects the graph at most once. In other words, no vertical line should intersect the graph at more than one point.
If you observe a graph and find any vertical line that intersects the graph at two or more points, then the graph does not represent a function. This suggests that there is at least one input value that corresponds to multiple output values, violating the definition of a function.
On the other hand, if every vertical line you draw intersects the graph at most once, then the graph represents a function. This implies that each input value corresponds to a unique output value, meeting the criteria for a function.
By applying the vertical line test to a graph, you can determine whether or not a function is shown.