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ghazi
 2 years ago
is the equation of ellipse a function?
ghazi
 2 years ago
is the equation of ellipse a function?

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jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2No 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.

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1okay ...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?

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1\[y=b * \sqrt (1x^2/a)\]

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2Circle (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)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2The last line gives it away that it can't be a function

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1okay...by the way what is the accurate and precised definition of function?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2A function is something that maps each input to EXACTLY ONE output

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2With ellipses and circles, inputs map to more than one output

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1well that is one one onto function

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2no, a one to one function is each input is mapped to one unique output

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2not sure what you mean

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2if you mean multiple inputs lead to the same output, then that's still a function

08bkrishna
 2 years ago
Best ResponseYou've already chosen the best response.1if you mean a manyttoone function, that is a proper function. a basic example would be x^2, where, e.g. 2 and 2 map to 4

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2it's a function if you only get one output per input

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1yes 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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2that's not a function since it fails the vertical line test

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2that's the equation x = y^2 or something similar to that

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1@jim_thompson5910 it could be a function if it gives you two output by one input as @08bkrishna said

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2btw, the parabola has to be upright to be a function Just because it's a parabola, it doesn't automatically make it a function

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1well x=y^2 is a parabola....no need to be upright

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2it isn't upright since it's sideways

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0in your example x is a function of y, but not vice versa

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1@eliassaab can you help with this...please ..and @jim_thompson5910 i said why do i need it to be upright? for considering it parabola?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2yes that terminology is correct TuringTest...but confusing because x is usually the input, which means that x=y^2 isn't a function

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1well 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...

08bkrishna
 2 years ago
Best ResponseYou've already chosen the best response.1@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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.2The 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?

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1yea agreed...thank you...it was a big confusion....special thanks to @jim_thompson5910 , @08bkrishna

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \frac {x^2} {a^2}+\frac {y^2} {b^2}=1 \]

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0For each value of x, except x=a or x=a, y has two values. So it is not a function.
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