Use a Graphing Utility to Graph the Function, Approximate the Relative

question 32

Multiple Choice

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. $f ( x ) = x ^ { 2 } - 4 x + 1$

• A) Decreasing on \(( - \infty , 2 )\) Increasing on \(( 2 , \infty )\) Relative minimum: \(( 2 , - 3 )\)
• B) Decreasing on \(( 3 , \infty )\) Increasing on \(( - \infty , 3 )\) Relative maximum: \(( 3,12 )\)
• C) Decreasing on \(( 0,2 )\) Increasing on \(( - \infty , 0 ) , ( 2 , \infty )\) Relative minimum: \(( 0,0 )\) Relative maximum: \(( 2 , - 4 )\)
• D) Decreasing on \(( - \infty , - 1 ) , ( 1 , \infty )\) Increasing on \(( - 1,1 )\) Relative minimum: \(( - 1 , - 1 )\) Relative maximum: \(( 1,3 )\)
• E) Decreasing on \(( 1 , \infty )\) Increasing on \(( - \infty , 1 )\) Relative minimum: \(( - 1,1 )\) Relative maximum: \(( 1,2 )\)

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Definitions:

Lac Operon

A gene regulatory mechanism in bacteria where the metabolism of lactose is controlled by the interaction of several genes and protein products.

Mutation

A change in the DNA sequence within an organism's genome, which can lead to variations in physical appearance, function, or behavior.

Lactose

A sugar present in milk and dairy products, consisting of glucose and galactose units.

Transcription

The process by which the information in a strand of DNA is copied into a new molecule of messenger RNA (mRNA).