Question

can someone please help me

Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of function in your answer.

Answer 1

do you have notes that has the definition of a function ?

Answer 2

no

Answer 3

but i know what it means a relationship or expression involving one or more variables

Answer 4

the vertical line test consists in checking whether a function f(x) has two or more values associated to a same x: f(x)=y1 and f(x)=y2. If this is the case, it is not a function because a same x has two values associated to it, and you essentially do not know which one to pick. On the other hand, the converse can be a function: g(y)=x1 and g(y)=x2, like sin(x) and cos(x) for instance.

Answer 5

thank you @P0sitr0n

Answer 6

Here is the definition
A function is a special relationship where each input has a single output.

that means each "x" value (the input) has only 1 "y" value (the output)

if you have two points on a vertical line (one point above the other), that means we have two points with the same x (input) but different y (outputs). that is not allowed for a function