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

question 24

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) \(\begin{array} { l }
• D = \{ ( x , y ) \mid 0 \leq x < \infty , 0 \leq y < \infty \} \\
• R = \{ z \mid 2 \leq z \}
• \end{array}\)

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Definitions:

Imbibition

Imbibition is the process of absorption of water by substances, causing them to swell without dissolving, critically initiating seed germination.

Vernalization

The process by which exposure to cold temperatures for a certain length of time induces a plant to flower.

Thigmomorphogenesis

An alteration of plant growth in response to mechanical stimuli, such as wind, rain, hail, and contact with passing animals.

Rhizomes

Underground plant stems that send out roots and shoots from its nodes, involved in vegetative reproduction and storage.