Find the range of the function $f ( x , y ) = \sqrt { x - y ^ { 2 } }$ .
A) $( 0 , \infty )$

B) $[ 0 , \infty )$
C) $( - \infty , 0 )$
D) $( - \infty , \infty )$
E) $( 1 , \infty )$
F) $[ 1 , \infty )$

G) $( \sqrt { 2 } , \infty )$

H) $[ \sqrt { 2 } , \infty )$

Question

Find the range of the function $f ( x , y ) = \sqrt { x - y ^ { 2 } }$ .
A) $( 0 , \infty )$
 
B) $[ 0 , \infty )$ 
C) $( - \infty , 0 )$ 
D) $( - \infty , \infty )$
E) $( 1 , \infty )$
F) $[ 1 , \infty )$

G) $( \sqrt { 2 } , \infty )$ 
 
H) $[ \sqrt { 2 } , \infty )$

Quizplus · Accepted Answer

The function $f(x, y) = \sqrt{x - y^2}$ involves a square root. The expression inside the square root, $x - y^2$, must be greater than or equal to 0 for the function to return real numbers. This means the smallest value the function can take is 0, when $x = y^2$. Since there is no upper limit to $x$, the function can approach infinity. Therefore, the range includes 0 and extends to infinity, which is represented by $[0, \infty)$.

Find the Range of the Function f(x,y)=x−y2f ( x , y ) = \sqrt { x - y ^ { 2 } }f(x,y)=x−y2​

Find the Range of the Function $f ( x , y ) = \sqrt { x - y ^ { 2 } }$