Question

Help with understanding a concept involving the graph of a function.

Answer 1

what concept?

Answer 2

So the graph x^2+y^2=1 does not describe y as a function of x.

Answer 3

why not?

Answer 4

yes it doesnt so what ?

Answer 5

But if we localize the view to certain areas (the circles areas), we can see the graph of a function.

Answer 6

I'm lost on why the areas at x=1 and x=-1 are not graphs of functions, while the other two points are.

Answer 7

x^2 + y ^2 = 1 means y ^2 = 1 - x^2, right?

Answer 8

actually you saying it in reverse

Answer 9

it meets the requirements of function, only at x = -1 and x = 1

Answer 10

everywhere else, it fails the vertical line test

Answer 11

Hm, my teacher is saying otherwise I think.

Answer 12

Go to 12:30 of this video: http://math.uh.edu/~jmorgan/Math1431/video/day11/day11.html

Answer 13

x^2 + y^2 = 1 is a curve on a graph such that every point on that curve, when squared and added results in the number 1.

Answer 14

can you think of any point that would solve this condition?

Answer 15

Hmm

Answer 16

0 and 1?

Answer 17

very good. what does 0 and 1 mean on a graph? where is the point (0,1) lie on the graph?

Answer 18

On the x-axis?

Answer 19

Oh, snap, yeah, y-axis. I knew that lol

Answer 20

no 0,1 means 0 in the horizontal direction and 1 in the vertical direction

Answer 21

okay. now, can you think of any other point?

Answer 22

0 and -1?

Answer 23

very good.

Answer 24

any other point?

Answer 25

(1,0) and (-1,0)?

Answer 26

yup.

Answer 27

But how does all this translate to those points not being functions on the graph?