Find the domain and range and describe the level curves for the function f(x,y).
-$$f ( x , y ) = \frac { y + 2 } { x ^ { 2 } }$$
A) Domain: all points in the $x y$-plane; range: real numbers $z \geq 0$; level curves: parabolas $y = c x ^ { 2 } - 2$
B) Domain: all points in the $x y$-plane excluding $x = 0$; range: real numbers $z \geq 0$; level curves: parabolas $y = c x ^ { 2 } - 2$
C) Domain: all points in the $x y$-plane excluding $x = 0$; range: all real numbers; level curves: parabolas $y = c x ^ { 2 } - 2$
D) Domain: all points in the $x y$-plane; range: all real numbers; level curves: parabolas $y = c x ^ { 2 } - 2$

Question

Quizplus · Accepted Answer

The function $f(x, y) = \frac{y + 2}{x^2}$ is undefined when $x = 0$, so the domain excludes any point where $x = 0$. The range is all real numbers because the numerator $y + 2$ can take any real value, making the fraction any real number as $x$ varies. The level curves are found by setting $f(x, y) = c$, leading to $y = cx^2 - 2$, which are parabolas.

Find the Domain and Range and Describe the Level Curves f(x,y)=y+2x2f ( x , y ) = \frac { y + 2 } { x ^ { 2 } }f(x,y)=x2y+2​

Find the Domain and Range and Describe the Level Curves $f ( x , y ) = \frac { y + 2 } { x ^ { 2 } }$