Give the Domain and Range for the Rational Function $$f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$$

question 408

Multiple Choice

Give the domain and range for the rational function. Use interval notation.
- $$f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$$

• A) Domain: \(( - \infty , 7 ) \cup ( 7 , \infty )\); Range: \(( - \infty , 0 )\)
• B) Domain: \(( - \infty , 7 ) \cup ( 7 , \infty )\); Range: \(( - \infty , 5 )\)
• C) Domain: \(( - \infty , 7 ) \cup ( 7 , \infty )\); Range: \(( 5 , \infty )\)
• D) Domain: \(( - \infty , - 7 ) \cup ( - 7 , \infty )\); Range: \(( - \infty , 5 )\)

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Definitions:

Rewarded

To receive something of value in recognition of service, effort, or achievement.

Categorical Proposition

A statement that affirms or denies something about all members of a category.

Conversion

In logic, a method of changing a categorical proposition by interchanging its subject and predicate without altering its truth value.

Obversion

A logical operation that involves changing a categorical statement into its obverse by negating both the subject and predicate and changing the quality of the statement from affirmative to negative, or vice versa.