Question

is the equation of ellipse a function?

Answer 1

No it is not. You can pass a vertical line through it and it will pass through more than one point. So it fails the vertical line test.

Answer 2

okay ...what if i write it as function of y ..i mean just consider standard equation of ellipse and separate both the variables..like y in terms of x....so can't we call it function?

Answer 3

y=bsqrt (1-x^2/a)

Answer 4

\[y=b * \sqrt (1-x^2/a)\]

Answer 5

Circle (special type of ellipse)

x^2 + y^2 = r^2

y^2 = r^2 - x^2

y = +-sqrt(r^2 - x^2)

y = sqrt(r^2 - x^2) or y = -sqrt(r^2 - x^2)

Answer 6

The last line gives it away that it can't be a function

Answer 7

okay...by the way what is the accurate and precised definition of function?

Answer 8

A function is something that maps each input to EXACTLY ONE output

Answer 9

With ellipses and circles, inputs map to more than one output

Answer 10

well that is one one onto function

Answer 11

no, a one to one function is each input is mapped to one unique output

Answer 12

and what about many one?

Answer 13

not sure what you mean

Answer 14

many one onto function?

Answer 15

if you mean multiple inputs lead to the same output, then that's still a function

Answer 16

if you mean a manyt-to-one function, that is a proper function. a basic example would be x^2, where, e.g. -2 and 2 map to 4

Answer 17

it's a function if you only get one output per input

Answer 18

yes that's what i mean and @jim_thompson5910 if i pass a vertical line through a parabola still it cuts parabola at two points isn't it a fucntion ...the equation of parabola?

Answer 19

that's not a function since it fails the vertical line test

Answer 20

that's the equation x = y^2 or something similar to that

Answer 21

@jim_thompson5910 it could be a function if it gives you two output by one input as @08bkrishna said

Answer 22

btw, the parabola has to be upright to be a function

Just because it's a parabola, it doesn't automatically make it a function

Answer 23

well x=y^2 is a parabola....no need to be upright

Answer 24

it isn't upright since it's sideways

Answer 25

in your example x is a function of y, but not vice versa

Answer 26

@eliassaab can you help with this...please ..and @jim_thompson5910 i said why do i need it to be upright? for considering it parabola?

Answer 27

yes that terminology is correct TuringTest...but confusing because x is usually the input, which means that x=y^2 isn't a function

Answer 28

well jim ...i have to check this out...especially your definition of function....cuz i know there is many one into function in which one input leads to many output...

Answer 29

@ghazi, a many to one function is where more that one input leads to the same output. this is different to a one to many, where one input leads to multiple outputs. the former is considered an equation, while the latter isn't

Answer 30

The whole point of the function is to predict the output. But if you get more than one output, then which output will you choose?

Ex: If I have a "function" of the price of a car (y) after some number of years (x), then which price will I choose if I get more than one outputs for a particular x value?

Answer 31

yea agreed...thank you...it was a big confusion....special thanks to @jim_thompson5910 , @08bkrishna

Answer 32

\[
\frac {x^2} {a^2}+\frac {y^2} {b^2}=1
\]

Answer 33

is it a function or not?

Answer 34

For each value of x, except x=a or x=-a, y has two values. So it is not a function.