Give the Domain and Range for the Rational Function $$f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$$

question 132

Multiple Choice

Give the domain and range for the rational function. Use interval notation.
- $$f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$$

• A) Domain: \(( - \infty , 5 ) \cup ( 5 , \infty )\); Range: \(( 0 , \infty )\)
• B) Domain: \(( - \infty , - 3 ) \cup ( - 3 , \infty )\); Range: \(( - \infty , 5 )\)
• C) Domain: \(( - \infty , 3 ) \cup ( 3 , \infty )\); Range: \(( - \infty , 0 ) \cup ( 0 , \infty )\)
• D) Domain: \(( - \infty , 3 ) \cup ( 3 , \infty )\); Range: \(( 5 , \infty )\)

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Definitions:

Public Goods

Goods that are non-excludable and non-rivalrous, meaning their consumption by one individual does not reduce availability to others.

Private Consumption

The total value of all goods and services consumed by individuals and households for personal use.

Pareto Efficient

A resource distribution condition where no reallocation can improve one person's situation without detrimentally affecting another person's situation.

Public Good

A good that is non-excludable and non-rivalrous, meaning it can be used by everyone and one person's use does not reduce its availability to others.