Why is a vertical line, rather than a horizontal line, used to determine if a graph represents a function?

Question

explain in words i can understand

Answer 1

perhaps it cause the slope of a vertical line cannot be determined(infinity)

that means the function cud be discontinous at that point!

so it helps

Answer 2

if a vertical line goes through the graph, then i think it is not a function, horizontal doesn't really matter. because if a vertical line goes through the graph, then the graph must be an ellipse, which means its not a function.

i hope that makes sense.

Answer 3

f(x) =x will be a function if for every value of domain (x values) there is a unique value in the range ( y values).

y values is represented by y-axis which is a vertical line

If a vertical line crosses the graph at more than one point that means for  a single value of x there are two value of y and this goes against the defn of a function.

on the other hand it doesnt matter if the input is many (x values) but the out put should be one for each(y values)

like , (2,4), (3,4), (-5,4) is a function

so in case of horizontal line there will be same output(y values) and may have different input(x values).

Answer 4

Because, if a vertical line passes through two or more points on any part of the graph at the same time, it would not be a function. This is because there are two (or more) outputs for every one input.