Give a Rule for the Piecewise-Defined Function B) $f ( x ) = \left\{ \begin{array} { l l } - x ^ { 3 } & \text { if } x < 1 \\ x - 2 & \text { if } x \geq 1 \end{array} \right.$

question 34

Multiple Choice

Give a rule for the piecewise-defined function. Then give the domain and range.
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• A) \(f ( x ) = \left\{ \begin{array} { l l } \sqrt [ 3 ] { x } & \text { if } x < 1 ; \text { Domain: } ( \infty , \infty ) , \text { Range: } ( \infty , 1 ) \cup [ 3 , \infty ) \\ x + 2 & \text { if } x \geq 1 \end{array} \right.\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } - x ^ { 3 } & \text { if } x < 1 \\ x - 2 & \text { if } x \geq 1 \end{array} \right.\) Domain: \(( \infty , 1 ) \cup [ 3 , \infty )\), Range: \(( \infty , \infty )\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \\ x + 2 & \text { if } x \geq 1 \end{array} \right.\) Domain: \(( \infty , \infty )\), Range: \(( \infty , 1 ) \cup [ 3 , \infty )\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \\ x - 2 & \text { if } x \geq 1 \end{array} \right.\); Domain: \(( \infty , 1 ) \cup [ 3 , \infty )\), Range: \(( \infty , \infty )\)

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The amount of money required to purchase a good or service, often determined by factors like supply, demand, and production cost.

Utility Function

A mathematical representation that associates levels of utility or satisfaction a consumer derives from consuming various bundles of goods.