Find the Domain and Range of the Function $$f ( x ) = 1 - x ^ { 2 }$$

question 421

Multiple Choice

Find the domain and range of the function.
- $$f ( x ) = 1 - x ^ { 2 }$$

• A) Domain: \(( - \infty , \infty )\); Range: \(( - \infty , - 1 ]\)
• B) Domain: \(( - \infty , \infty )\); Range: \([ 1 , \infty )\)
• C) Domain: \(( - \infty , \infty )\); Range: \(( - \infty , 1 ]\)
• D) Domain: \(( - \infty , 1 ]\); Range: \([ - 1 , \infty )\)

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Definitions:

Cinnamaldehyde

A yellow oily compound that gives cinnamon its flavor and odor, known chemically as a phenylpropanoid.

Claisen Product

The β-keto ester or β-diketone result obtained from a Claisen Condensation reaction.

Methyl Phenylacetate

An organic compound characterized by an ester functional group connecting a methyl group and a phenylacetate group.

Aldol Reaction

A type of chemical reaction in which an enolate ion reacts with a carbonyl compound to form a β-hydroxyaldehyde or β-hydroxyketone, followed often by dehydration to give a conjugated enone.