So, as I was learning about functions, it said that there are functions that can be odd and even at the same time, but I seriously don’t understand why the function x^2+y^2=1 can be both;
It is indeed even: f(-x)=(-x^2)+y^2=x^2+y^2=1=f(x)
And to to test if it is odd: -f(x)=-(x^2+y^2)=-x^2-y^2 which isn’t equal to f(-x)
Can anyone explain what am I doing wrong?
✅ Answers
Answerer 1
even functions are symmetrical around the y axis
odd functions are symmetrical around the origin
this example is actually the equation for a circle with a radius of 1 with (0, 0) as the center
it is both symmetric around y axis and the origin
(x – 0)^2 + (y – 0)^2 = 1^2
x^2 + y^2 = 1
Answerer 2
Function of a Circle.
If x= -2, f(-2) = 4 + y^2
Same as for x=2.
You are not squaring-2, you must be doing -(2)^2, hence the difference.
Thus -f(2) = -(4+y^2)= -4- y^2, the same as (-2)^2 – y^2 =(-) 4- y^2 which does equal -4- y^2
Source(s):
I am a Senior Maths & Science teacher
Answerer 3
x^2+y^2=1 is not a function, it is a relation, so you cannot call
it either an odd or an even function.