Question

The unit circle with center at the origin is a relation but not a function Find the two functions which are semicircles of the unit circle and determine their domains and ranges?​

Answer 1

Explanation:

The relation is x²+y²=r² with r being the radius

`f(x)=y=√(r^2-x^2) \\\\domain(f(x))=[-r,r]\ or\ -r\leq x \leq r\\range(f(x))=[0,r]\ or\ 0\leq y \leq r\\\\\\\ g(x)=y=-√(r^2-x^2) \\domain(g(x))=[-r,r]\ or\ -r\leq x \leq r\\range(g(x))=[-r,0]\ or\ -r\leq y \leq 0\\\\`