Question

Decide whether the equation defines y as a function of x.
x^{2}y-x^{2}+3y=0
How to know whether y is a funtion of x or not?

Answer 1

Theoretically, if you pick a value for 'x', do you EVER get more than one value for 'y'?

More Practically, can you solve it for y and get a better look at it?

Answer 2

sorry i still don't get it, can you explain it more ):

Answer 3

You didn't answer my question. Can you solve it for 'y'? Let's see what you get.

Answer 4

if x=1 then y=1/4, yes, only one value, and what to do next?

Answer 5

That is quite insufficient. You must pick all possible values for x and prove it for all of them.

Go ahead and solve it for y. You will see it clearly in that form.

Answer 6

after that, do i need to graph it and use the vertical line test?

Answer 7

@tamiashi try rearranging the equation into the form y = ...

Answer 8

You shouldn't need to graph it for the vertical line test, but you can if you like. It's usually obvious from the equation, as to whether it's a function or not.

Answer 9

Writing it this way might help you to solve for y...\[(x^{2}y + 3y) -x^{2}=0 \]

Answer 10

y=x^2/x^2 + 3, and then?

Answer 11

Very bad: y = x^2 / (x^2 + 3) is correct.

The parentheses are NOT optional.

Think on this expression on the right hand side. Given a value for x, and and all possible values, will you EVER get more than one value for y?

Answer 12

\[(x^{2}y + 3y) -x^{2}=0 \]try pulling a factor of y from above to get...
\[y(x^{2} + 3) -x^{2}=0\]Now try solving for y.

Answer 13

@agent0smith y= x^2/(x^2+3) i missed the parentheses as tkhunny said ><
@tkhunny Hm... if there is no more than one value for y, then y is a funtion of x, isn't it?

Answer 14

Yes. Can you talk your way to that conclusion or will you just be assuming it?