Find the domain and range of the function $h ( x , y ) = \sqrt { 2 x - 9 y }$ .
A) $\begin{array} { l }
D = \left\{ ( x , y ) \mid y \geq \frac { 9 } { 2 } x \right\} \
R = \{ z \mid 0

Question

Find the domain and range of the function $h ( x , y ) = \sqrt { 2 x - 9 y }$ .
A) $\begin{array} { l } 
D = \left\{ ( x , y ) \mid y \geq \frac { 9 } { 2 } x \right\} \
R = \{ z \mid 0 < z \}
\end{array}$
B) $\begin{array} { l } 
D = \left\{ ( x , y ) \mid y \leq \frac { 2 } { 9 } x \right\} \
R = \{ z \mid 0 < z \}
\end{array}$
C) $\begin{array} { l } 
D = \left\{ ( x , y ) \mid y \leq \frac { 2 } { 9 } x \right\} \
R = \{ z \mid 0 \leq z \}
\end{array}$
D) $\begin{array} { l } 
D = \left\{ ( x , y ) \mid y \geq \frac { 9 } { 2 } x \right\} \
R = \{ z \mid 0 \leq z \}
\end{array}$

Quizplus · Accepted Answer

The domain is determined by the condition under the square root being non-negative: $2x - 9y \geq 0$, which simplifies to $y \leq \frac{2}{9}x$. The range of the square root function is all non-negative real numbers, so $R = \{ z \mid 0 \leq z \}$.

Find the Domain and Range of the Function h(x,y)=2x−9yh ( x , y ) = \sqrt { 2 x - 9 y }h(x,y)=2x−9y​

Find the Domain and Range of the Function $h ( x , y ) = \sqrt { 2 x - 9 y }$