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

Understand the regulatory framework surrounding monopolies and public utilities.

Examine the economic justifications for patents and government-sanctioned monopolies.

Analyze the impact of breaking up monopolies on market outcomes.

Understand the concept of economies of scale as it applies to monopolistic markets.

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Definitions:

Cognitive Distortion

Patterns of thinking that are biased, irrational, or inaccurate, often leading to misinterpretation of reality and negatively impacting mental health.

Bulimia

An eating disorder characterized by episodes of binge eating followed by purging to try to control weight.

Overgeneralization

A cognitive distortion where an individual applies a general rule too broadly, often evident in language acquisition or in forming beliefs about the world based on limited experiences.

Psychoanalytic Approach

A method of psychological theory and therapy that aims to treat mental disorders by investigating the interaction of conscious and unconscious elements in the mind.