Question

Check whether the followings represent function or not

(i) $x^2+y^2=36, \quad y \in[0,6]$

(ii) $x^2+y^2=36, \quad x \in[0,1]$

(iii) $\quad x^2+y^2=36, \quad x \in[-6,6]$

(iv) $x^2+y^2=36$

Answer 1

$x^2+y^2=36 \quad \Rightarrow \quad y= \pm \sqrt{36-x^2}$

Equation represents circle of radius 6 with centre $(0,0)$

By vertical line test, for every value of $x$, there are two values of $y$.

Which contradicts definition of function

So equation doesn't represents a function.