Question

I don't know what to do with this problem.

It's 3x-y^2=16

It wants to know if it's a function. I know what a function is, and how to figure out if an equation is a function, and why or why it may not be, but this one stumps me.

Answer 1

of course it is not a function
it is an equation

Answer 2

-y^2=16-3x
y^2=3x-16
y=sqrt(3x-16)

Answer 3

the real question is, if you solve for \(y\) what do you get
lets do it carefully

Answer 4

this is a function @satellite73

Answer 5

ur no

Answer 6

oh yeah

Answer 7

\[ 3x-y^2=16 \]is an equation, it is not a function
the person who wrote this question is confused, but what should really be asked is can \(y\) be function of \(x\) and the answer is NO

Answer 8

\[3x-y^2=16\\
3x-16=y^2\\
\pm\sqrt{3x-16}=y\] and the \(\pm\) tells you x is not a function of y

Answer 9

or rather y is not a function of x

Answer 10

Oh wait, I'm sorry, I forgot the 4. The equation is actually 3x-4y^2=16.

@satellite73 Equations are functions. You plug in x values to get y values. An equation is a function if only one y value comes out per x value.

Answer 11

right the 4 makes no difference the answer is still NO because of the square on the y

Answer 12

The 4 makes a difference in the equation, though. So, what does the equation turn out to be when solving for y?

Answer 13

ahhh thus begins the confusion between equations and functions
functions CAN be given by equations, but they do not have to be
and all equations are not functions

Answer 14

\[ 3x-4y^2=16. \\
3x-16=4y^2\\
\frac{3x-16}{4}=y^2\\
\pm\frac{\sqrt{3x-16}}{2}=y\]

Answer 15

I know that, I didn't say all equations were, I just said that equations can be functions, too.

Answer 16

in any case it is the \(\pm\) that throws it off
be careful when solving with a square
common mistake would be to write
\[y=\frac{\sqrt{3x-16}}{2}\] and forget about the \(\pm\) part

Answer 17

another way to see it is not a function is to know that this is a parabola that opens to the right, so does not pass the vertical line test
http://www.wolframalpha.com/input/?i=3x-y^2%3D16+

Answer 18

So, the question still remains, is this a function. Does every x input have only one y output?

Answer 19

and the answer is NO
we can do it by example if you like

Answer 20

can we find two different y values that come from the same x value in other words, and the answer is yes we can
pick an x and we can find the two y values

Answer 21

I graphed it on my graphing calculator, and got half a sideways parabola, meaning it would pass the vertical line test.

Answer 22

did you get something like this ?

Answer 23

No, like I just said, I got half a sideways parabola.

Answer 24

that is because your graphing calculator only graphs functions, so it probably graphed the top half only

Answer 25

like i said, the square on the y is what makes it not a function
just like \(x=y^2\) is not a function since if \(x=25\) \(y=5\) or \(y=-5\) both work