Sketch graph for two variable

Question

Find domaine and range then sketch the graph for two variable:  the question one is Z²=x²+y²      the question number two is y=Z²

Answer 1

Hi Mzhda, the equation z² = x² + y², is the standard form of the circle with radius of z. y = z² is a parabola.

 

Circle: z² = x² + y²:

 

Domain: 

 

The domain of the circle is: {-z, z}.

 

Range:

 

The range of the circle is: {-z, z}.

 

Parabola: y = z²:

 

Domain:

 

The domain of the parabola is; {-∞, ∞}.

 

Range:

 

The range of the parabola is: {0, ∞}.

 

Questions?