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ghazi

is the equation of ellipse a function?

  • one year ago
  • one year ago

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  1. jim_thompson5910
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    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.

    • one year ago
  2. ghazi
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    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?

    • one year ago
  3. ghazi
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    y=bsqrt (1-x^2/a)

    • one year ago
  4. ghazi
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    \[y=b * \sqrt (1-x^2/a)\]

    • one year ago
  5. jim_thompson5910
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    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)

    • one year ago
  6. jim_thompson5910
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    The last line gives it away that it can't be a function

    • one year ago
  7. ghazi
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    okay...by the way what is the accurate and precised definition of function?

    • one year ago
  8. jim_thompson5910
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    A function is something that maps each input to EXACTLY ONE output

    • one year ago
  9. jim_thompson5910
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    With ellipses and circles, inputs map to more than one output

    • one year ago
  10. ghazi
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    well that is one one onto function

    • one year ago
  11. jim_thompson5910
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    no, a one to one function is each input is mapped to one unique output

    • one year ago
  12. ghazi
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    and what about many one?

    • one year ago
  13. jim_thompson5910
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    not sure what you mean

    • one year ago
  14. ghazi
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    many one onto function?

    • one year ago
  15. jim_thompson5910
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    if you mean multiple inputs lead to the same output, then that's still a function

    • one year ago
  16. 08bkrishna
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    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

    • one year ago
  17. jim_thompson5910
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    it's a function if you only get one output per input

    • one year ago
  18. ghazi
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    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 |dw:1345840885553:dw| isn't it a fucntion ...the equation of parabola?

    • one year ago
  19. jim_thompson5910
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    that's not a function since it fails the vertical line test

    • one year ago
  20. jim_thompson5910
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    that's the equation x = y^2 or something similar to that

    • one year ago
  21. ghazi
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    @jim_thompson5910 it could be a function if it gives you two output by one input as @08bkrishna said

    • one year ago
  22. jim_thompson5910
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    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

    • one year ago
  23. ghazi
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    well x=y^2 is a parabola....no need to be upright

    • one year ago
  24. jim_thompson5910
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    it isn't upright since it's sideways

    • one year ago
  25. TuringTest
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    in your example x is a function of y, but not vice versa

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

    • one year ago
  27. jim_thompson5910
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    yes that terminology is correct TuringTest...but confusing because x is usually the input, which means that x=y^2 isn't a function

    • one year ago
  28. ghazi
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    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...

    • one year ago
  29. 08bkrishna
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    @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

    • one year ago
  30. jim_thompson5910
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    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?

    • one year ago
  31. ghazi
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    yea agreed...thank you...it was a big confusion....special thanks to @jim_thompson5910 , @08bkrishna

    • one year ago
  32. eliassaab
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    \[ \frac {x^2} {a^2}+\frac {y^2} {b^2}=1 \]

    • one year ago
  33. ghazi
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    is it a function or not?

    • one year ago
  34. eliassaab
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    For each value of x, except x=a or x=-a, y has two values. So it is not a function.

    • one year ago
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