How do I know if it's a function?

Question

How do i know if this equation is a function without graphing?

2y= 3/x

Answer 1

It's a function if for every x value there is one and only one "y" value that you could have.  It's OK if more than one x value shares the same y value, but you can't have 2 or more y values for one single x value.

Think of it this way:

y = 3 / (2x)

y = (x * (2/3))^-1

If you take a number, multiply it by 2/3, and take the reciprocal, then there's no way you get a different result unless you change the original number.  For every x, multiplying the number by 2/3 and inverting the result is a method that can only give you one value each time.

Something like |y| = x isn't a function, because for example if x = -5 then you could have y = -5 or y = 5.

Answer 2

when you get a new value for y for every x.  that is a function

Answer 3

um simpler way of looking at it is isolating y

~ y = 3/2x

now if you were to put any number for x there can be only 1 y

and example where it cant be a function is square roots where if you square root something it can be + or -

but absolute " l#l " can be a function because say

y = lxl

if x were 5 and - 5 y is still 5 for both but it's still a function because 2 x's can be 1 y but 1 x cannot be two y's

think of it like a soda machine

if you press the sprite button you want to get sprite not a chance of either sprite or coke

but on a soda machine there are more than one sprite buttons that give you the same sprite

and the coke buttons will give you coke not a coke or a sprite

buttons = x

what you get = y