## sakigirl 2 years ago Is y=x^2+4 a function? How do you know?

1. abb0t

Of course it's a function!

2. abb0t

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

3. sakigirl

Vertical line test?

4. sakigirl

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

5. abb0t

|dw:1359706054639:dw|

6. skullpatrol

Have you checked the definition of a "function"?

7. sakigirl

yes

8. skullpatrol

What does does it say?

9. sakigirl

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

10. skullpatrol

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

11. sakigirl

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

12. abb0t

buuurn!

13. sakigirl

lol, it's just a question

14. skullpatrol

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

15. sakigirl

Oh, I understand now! Thanks :)

16. sakigirl

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?

17. campbell_st

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

18. sakigirl

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

19. abb0t

BUUUUUURN!!!!

20. sakigirl

omg it's just a correctionnn

21. campbell_st

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

22. sakigirl

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

23. skullpatrol

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

24. sakigirl

Wait @campbell_st how did you get that graph?

25. abb0t

26. 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...

27. sakigirl

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

28. skullpatrol

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

29. sakigirl

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

30. sakigirl

*how do you get the function for this line

31. sakigirl

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

32. 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...

33. sakigirl

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

34. sakigirl

?

35. 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

36. sakigirl

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

37. campbell_st

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

38. campbell_st

yes he was...

39. sakigirl

Thank you :) You made it clear for me

40. abb0t

|dw:1359707283237:dw|

41. campbell_st

42. 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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