Find the Domain and Range of the Function $g ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } + 3$

question 141

Multiple Choice

Find the domain and range of the function $g ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } + 3$ .

• A)
• \[\begin{array} { l }
• D = \{ ( x , y ) \mid 0 \leq x < \infty , 2 \leq y < \infty \} \\
• R = \{ z \mid 0 \leq z \}
• \end{array}\]
• B)
• \[\begin{array} { l }
• D = \{ ( x , y ) \mid - \infty < x < \infty , - \infty < y < \infty \} \\
• R = \{ z \mid 3 \leq z \}
• \end{array}\]
• C)
• \[\begin{array} { l }
• D = \{ ( x , y ) \mid - \infty < x < \infty , 2 \leq y < \infty \} \\
• R = \{ z \mid - \infty < z < \infty \}
• \end{array}\]
• D)
• \[\begin{array} { l }
• D = \{ ( x , y ) \mid 0 \leq x < \infty , 0 \leq y < \infty \} \\
• R = \{ z \mid 2 \leq z \}
• \end{array}\]

---

Definitions:

Linear Association

A relationship between two variables where a change in one variable is associated with a proportional change in the other variable.

Covariance

A measure of linear association between two variables. Positive values indicate a positive relationship; negative values indicate a negative relationship.

Variables

Elements, features, or factors that are capable of changing or varying across different conditions or within different individuals in a study.

Population Standard Deviation

A measure of the dispersion of a dataset relative to its mean, calculated for the entire population.