Why does y=3 represent a function, but x=3 does not?

Question

i know x=3 makes a verticle line but doesnt it not matter because you dont know if there are more than one points on that x=3 line

Answer 1

There are infinitely many points on that line! Hence it's not a function.

A function can only have one y value for any x value

Answer 2

Because x = 3 means any ordered pair with x coordinate of 3 is included, such as (3,4) or (3,5),  but to be a function no two different ordered pairs can have the same x coordinate.

However, y = 3 only means the y coordinate must be 3, like (5,3) or (6,3), and all those points have different x coordinates so it's a function.

Answer 3

X=3 means a straight line parallel to y axis. If you use a single line method(drawing a line parallel to y axis and see on how many points it cuts the line) you see that every point is cut but for y=3, only one point is cut. Technically that's why y=3 is a function but x=3 isn't...

  

Answer 4

In a function of x, every x-value should correspond to one and only one y-value.  When x=3, more than one y-value corresponds, because the vertical line is infinite, and, therefore x=3 is not a function.  Y=3 is a function of x because it is an infinite horizontal line, and each x-value has only one y-value, even though they're all the same.

Answer 5

Because a function is defined as something that takes an independent value ("x") and assigns to it one and only one dependent value ("y").  The line x=3 includes the points (3,1), (3,2), (3,3), etc. so you can have more than one y value for the same x value.  That's not the case with y=3.  Every x value has only one y value paired with it.  It doesn't matter that there are other x values that have the same y value.