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

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

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

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

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

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

well that is one one onto function

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

and what about many one?

not sure what you mean

many one onto function?

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

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

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

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

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

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

it isn't upright since it's sideways

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

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

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

is it a function or not?

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

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