How many explicit functions y= f(x) does the implicit relation x^2 + y^2 = 5 determine?

Question

A) 0

B) 1

C) 2

D) Infinite

Answer 1

The graph of x² + y² = 5 is a circle with center (0,0) and radius √5.

 

There are 2 explicit functions determined, the upper semicircle and the lower semicircle.

 

To obtain the equations of the functions, solve for y:

 

   y² = 5 - x²     So, y = ±√(5-x²)

 

   The functions are y = √(5-x²) and y = -√(5- x²).