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

question 36

Multiple Choice

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

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

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Definitions:

Achondroplasia

A genetic disorder characterized by dwarfism, specifically affecting bone growth and resulting in disproportionately short limbs.

Homozygous

Having two identical alleles at the same locus on homologous chromosomes.

Phenylketonuria (PKU)

A genetic disorder characterized by the inability to metabolize the amino acid phenylalanine, leading to brain and developmental issues if untreated.

Diet Low

Referring to a nutritional plan that reduces or limits the intake of a specific component, such as fat, carbohydrates, or calories.