Is y=x^2+4 a function? How do you know?

- anonymous

Is y=x^2+4 a function? How do you know?

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- schrodinger

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- abb0t

Of course it's a function!

- abb0t

If it passes the vertical line test, it's a function.

- anonymous

Vertical line test?

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- anonymous

I checked the answer key, and it's not a function..

- abb0t

|dw:1359706054639:dw|

- skullpatrol

Have you checked the definition of a "function"?

- anonymous

yes

- skullpatrol

What does does it say?

- anonymous

A function is a special relationship between values: Each of its input values gives back exactly one output value.

- skullpatrol

Set up a table of values like ...-3, -2, -1, 0, 1, 2, 3, .. and test it.

- anonymous

How does that let me know whether it's a function or not?

- abb0t

buuurn!

- anonymous

lol, it's just a question

- skullpatrol

Does each input value give "back exactly one output value."???

- anonymous

Oh, I understand now! Thanks :)

- anonymous

But, won't I have to try out all of the numbers? What if somewhere along the line, the x has more than one y value?

- campbell_st

are you sure you haven't entered the equation incorrectly
perhaps it should be
\[x= y^2 + 4\]

- anonymous

No, that is incorrect. The y value is always the output.

- abb0t

BUUUUUURN!!!!

- anonymous

omg it's just a correctionnn

- campbell_st

no its a graph that looks like
|dw:1359706698575:dw|

- anonymous

Well, that's the reflection of y=x^2+4 over the y axis, but no that's not correct. I have the answer key

- skullpatrol

Once you try a few input values you will be able to draw a "graph" like above...

- anonymous

Wait @campbell_st how did you get that graph?

- abb0t

##### 1 Attachment

- campbell_st

It the graph of \[x = y^2 + 4\]
which isn't a function and that's why I asked if you had typed in the correct equation.
Because the equation you have entered for the question is definitely a function...

- anonymous

Oh yes! Yes, that is what I meant.
I have a question for you!

- skullpatrol

Once you try a few input values you will be able to draw a "graph" of the output values.

- anonymous

how do you get function for this line? |dw:1359707035624:dw|

- anonymous

*how do you get the function for this line

- anonymous

Like, how did you know it was x=y^2+4?

- campbell_st

yep... so as @abb0t said... if you use a vertical line you can see it cuts the curve twice... so its not a function...
if the vertical like only cuts once you have a function...

- anonymous

For all we know, couldn't it have been y=(x+4)^2

- anonymous

?

- campbell_st

because you said that the answer was... not a function..
which to me you have transposed the x and y....
just an experience thing

- anonymous

The vertical line test made it so much easier! So @abb0t was correct in the first place :P

- campbell_st

and any parabola with x as the independent variable will be a function..

- campbell_st

yes he was...

- anonymous

Thank you :) You made it clear for me

- abb0t

|dw:1359707283237:dw|

- campbell_st

glad to help

- skullpatrol

Or the answer key is wrong...the important thing is to know to use the definition:
A function is a special relationship between values: Each of its input values gives back exactly one output value.

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