Why does the vertical line test work?
Please read the explanation.
Let us say we have a graph drawn for a mathematical relation.
This is a mathematical relation, as for every value of
To check whether this graph is a function, a Vertical Line Test can be used.
Let us examine the following graph drawn for the mathematical relation:
Can you observe the vertical lines drawn for various values of
All of these vertical lines intersect the graph at one point only.
If there is just one point of intersection,
that would mean,
for every x-value, there is just one unique y-value.
This property proves that the given mathematical relation
is a mathematical function.
Hence, the vertical line test works in determining whether a given relation is a function.
Let us try one more mathematical relation:
This mathematical relation creates a parabola and the parabola is symmetric about the x-axis, at
This mathematical relation
as the vertical line test fails.
Hope it helps.