Question

why does the vertical line test tell us whether the graph of a relation represents a function​

Answer 1

if a vertical line intersects at 2 points on the curve...that means....we get 2 values of y from the same x.....which is manyone type of relation

manyone type of relation are not functions

if u still have any doubt then plz do ask buddy;)

Answer 2

Answer:

A relation is a function of a vertical line if it crosses the graph at one and only one point. Otherwise the graph fails the vertical line test and therefore is not a function

Step-by-step explanation:

• The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.

Working

• The vertical line test supports the definition of a function. That is, every $x-value$ of a function must be paired to a single y-value. If we think of a vertical line as an infinite set of $x-values$, then intersecting the graph of a relation at exactly one point by a vertical line implies that a single$x-value$ is only paired to a unique value of y.
• The vertical line test is basically a way to see if a given input could provide multiple outputs. This is used to determine whether the mathematics you’re dealing with is, in fact, a function, or if it’s just an expression.
• A relation is a function of a vertical line if it crosses the graph at one and only one point. Otherwise the graph fails the vertical line test and therefore is not a function

• In contrary, if the vertical line intersects the graph more than once this suggests that a single xx-value is being associated with more than one value of y. This condition causes the relation to be “disqualified” or not considered as a function.
• If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
• Here are some examples of relations that are also functions because they pass the vertical line test.
• Cutting or Hitting the Graph at Exactly One Point

Graph of the line$f\left( x \right) = x + 1$

If a vertical line intersects the graph in some places at more than one point, then the relation is NOT a function.Here are some examples of relations that are NOT functions because they fail the vertical line test.

Cutting or Hitting the Graph in More Than One Point

Graph of the “sideway” parabola $x = {y^2}$